Bernoulli Bibliography

L


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L. R.M.: see SINGH A.P., L. R.M.

LACROIX S.F.,
[1] Traité des différences, Paris, 1819, t.2.

LAFORGIA A.,
[1] Inequalities for Bernoulli and Euler numbers, Boll. Un. Mat. Ital. A(5), 17 (1980), no. 1, 98-101.
Z498.10011; M81g:10028; R1980,11V466

LAGRANGE R.,
[1] Mémoire sure les suites de polynomes. Acta Math., 51 (1928), 201-309.
J54.0484.01

LAI K.F.: see EIE M., LAI K.F.

LAMPE E.,
[1] Auszug eines Schreibens an Herrn Stern über die Verallgemeinerung einer Jacobi'schen Formel, J. Reine Angew. Math., 84 (1878), 270-272.
J09.0176.03

LAMPE E.: see also BARNIVILLE J.J., DICKSON J.D.H., LAMPE E.

LAN YIZHONG,
[1] A limit formula for $\zeta(2k+1)$. J. Number Theory, 78 (1999), no. 2, 271-286.
Z949.11041; M2000f:11102

LANG H.,
[1] Über eine Gattung elementar-arithmetischer Klasseninvarianten reell-quadratischer Zahlkörper, J. Reine Angew. Math., 233 (1968), 123-175.
Z165.36504; M39#168; R1969,10A72

[2] Über Anwendungen höherer Dedekindscher Summen auf die Struktur elementar-arithmetischer Klasseninvarianten reell-quadratischer Zahlkörper, J. Reine Angew. Math., 254 (1972), 17-32.
Z244.12012; M45#8637; R1972,12A141

[3] Über Bernoullische Zahlen in reell-quadratischen Zahlkörpern, Acta Arith., 22 (1973), 423-437.
Z231.12004; M47#6651; R1973,11A120

[4] Über verallgemeinerte Bernoullische Zahlen und die Klassenzahl reell-quadratischer Zahlkörper, Acta Arith., 23 (1973), 13-18.
Z231.12005; M48#3914; R1974,1A175

[5] Über die Klassenzahlen eines imaginären bizyklischen Zahlkörpers und seines reell-quadratischen Teilkörpers, 2, J. Reine Angew. Math., 267 (1974), 175-178.
Z285.12013; M49#7238; R1974,12A133

[6] Über verallgemeinerte Dedekindsche Summen, Strahlklasseninvarianten reell-quadratischer Zahlkörper und die Klassenzahl des q-ten Kreisteilungskörpers, J. Reine Angew. Math., 338 (1983), 95-106.
Z506.12010; M84m:12006; R1983,7A151

[7] Über die Werte $\zeta (2-p,K)$ der Zetafunktion einer Idealklasse aus einem reell-quadratischen Zahlkörper, J. Reine Angew. Math., 361 (1985), 35-46.
Z559.12008; M87g:11153; R1986,4A397

[8] Über die Restklasse modulo $2^{e+2}$ des Wertes $2^en{\zeta}(1-2^en, K)$ der Zetafunktion einer Idealklasse aus dem reell-quadratischen Zahlkörper $ Q(\sqrt(D))$ mit $D \equiv 3 (mod 4)$, Acta Arith., 51 (1988), 277-292.
Z621.12014; M89i:11125; R1989,6A128

[9] Kummersche Kongruenzen für die normierten Entwicklungskoeffizienten der Weierstrassschen $\wp$-Funktion. Abh. Math. Sem. Univ. Hamburg, 33 (1969), no. 3-4, 183-196.
Z183.31304; M41#6780; R1970,3B71

[10] Über die Werte der Zetafunktionen einer Idealklasse und die Kongruenzen von N. C. Ankeny, E. Artin und S. Chowla für die Klassenzahl reell-quadratischer Zahlkörper. J. Number Theory, 48 (1994), no. 1, 102-108.
Z810.11062; M95i:11133

LANG S.,
[1] Elliptic Functions, Addison-Wesley, London, 1974. xiii + 326 pp.
Z316.14001; M53#13117; R1975,9A353

[2] Introduction to Modular Forms, Springer-Verlag, Berlin, 1976, Ch. 6, 10, 13.
Z344.10011; M55#2751; R1977,7A118K

[3] Cyclotomic fields. Graduate Texts in Mathematics, Vol. 59. Springer-Verlag, New York, 1978.
Z395.12005; M58#5578; R1979,11A312K

[4] Cyclotomic fields. II. Graduate Texts in Mathematics, 69. Springer-Verlag, New York, 1980.
Z435.12001; M81i:12004; R1981,9A274K

[5] Units and class groups in number theory and algebraic geometry, Bull. Amer. Math. Soc., 6 (1982), no. 3, 253-316.
Z482.12002; M83m:12002; R1983,1A344

[6] Introduction to Arakelov theory. Springer-Verlag, New York-Berlin, 1988. x+187 pp.
Z667.14001; M89m:11059

[7] Old and new conjectured Diophantine inequalities, Bull. Amer. Math. Soc. (N.S.), 23 (1990), no. 1, 37-75.
Z714.11034; M90k:11032

[8] Cyclotomic Fields I and II. Combined second edition. With an appendix by Karl Rubin. Graduate Texts in Mathematics, 121. Springer Verlag, Berlin etc., 1990, xviii+433p.
Z704.11038; M91c:11001

LANG S.: see also KUBERT D., LANG S.

LANGMANN K.,
[1] Eine endliche Formel für die Anzahl der Teiler von $n$. J. Number Theory, 11 (1979), no. 1, 116-127.
Z397.10038; M80g:10044; R1979,9A90

LAPLACE P.-S.,
[1] Mémoire sur l'usage du calcul aux différences partielles dans la théorie des suites, Mém. de math. et phys. Acad. Sci. (Paris), (1777), 99-122.

LASSÁK M.: see JAKUBEC S., LASSÁK M.

LE MAOHUA,
[1] A note on the generalized Bernoulli sequences, Ars Combin., 44 (1996), 283-286.
Z888.11010; M97g:05005; R1997, 11B184

LE BESGUE V.A.,
[1] Note sur les nombres de Bernoulli, C.R. Acad. Sci., Paris, 58 (1864), 853-856, 937-938.

LE BIHAN P.,
[1] L'équation diophantienne $m^q = \sum_{x=0}^{n-1}(kx+1)^p$, preprint, Mathématiques, Faculté des Sciences, Brest (France).

[2] Sur un résultat de J.J. Schäffer concernant l'équation $\sum_{k=1}^nk^p = m^q$, preprint, Mathématiques, Faculté des Sciences, Brest (France).

[3] L'équation $m^q = \sum_{x=0}^{n-1}(kx+1)^p$ , preprint, Mathématiques, Faculté des Sciences, Brest (France).

LECLERC M.: see BUTZER M. et al

LEE D.H.: see JANG L.C., KIM J.H., KIM T., LEE D.H., PARK D.W., RYOO C.S.

LEE DEOK-HO: see also JANG LEE-CHAE, KIM TAEKYUN, LEE DEOK-HO, PARK DAL-WON.

LEE JUNGSEOB,
[1] Integrals of Bernoulli polynomials and series of zeta function, Commun. Korean Math. Soc. 14 (1999), no. 4, 707-716.
Z0972.11011; M2000m:11020

LEE WILL Y.
[1] On fractional Bernoulli numbers. Kyungpook Math. J. 44 (2004), no. 1, 69-75.
M2004m:11021

LEEMING D.J.,
[1] Some properties of a certain set of interpolating polynomials, Canad. Math. Bull. 18 (1975), no. 4, 529-537.
Z317.41003; M53#1098; R1977,10V374

[2] An asymptotic estimate for the Bernoulli and Euler numbers, Canad. Math. Bull., 20 (1977), no. 1, 109-111.
Z358.10006; M56#5412; R1978,1V470

[3] The real zeros of the Bernoulli polynomials, J. Approx. Theory, 58 (1989), no. 2, 124-150.
Z692.41006; M90k:33029; R1990,4B130

[4] The coefficients of sinh $xt/\sin t$ and the Bernoulli polynomials. Internat. J. Math. Ed. Sci. Tech. 28 (1997), no. 4, 575-579.
Z970.56671; M98m:33023

LEEMING D.J., MACLEOD R.A.,
[1] Some properties of generalized Euler numbers, Canad. J. Math., 33 (1981), no. 3, 606-617.
Z419.10017; M82j:10025; R1982,4V517

[2] Generalized Euler number sequences: asymptotic estimates and congruences, Canad. J. Math., 35 (1983), no. 3, 526-546.
Z493.10015; M85c:11021; R1984,11A36

LEGENDRE A.M.,
[1] Traité des fonctions elliptiques, 1, Paris, 1825.

LEHMER D.H.,
[1] Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Ann. of Math. (2) 36 (1935), no. 3, 637-649.
J61.0066.01; Z12.15103

[2] An extension of the table of Bernoulli numbers, Duke Math. J., 2 (1936), 460-464.
J62.0050.05; Z15.00303

[3] On the maxima and minima of Bernoulli polynomials, Amer. Math. Monthly, 47 (1940), 533-538.
J66.0319.04; M2-43a

[4] The lattice points of an $n$-dimensional tetrahedron, Duke Math. J. 7 (1940), 341-353.
Z024.14901; M2,149g

[5] Generalized Eulerian numbers, J. Combinat. Theory, Ser. A, 32 (1982), no. 2, 195-215.
Z484.05006; M83k:10026; R1982,11V558

[6] Some properties of the cyclotomic polynomial, J. Math. Anal. Appl., 15 (1966), 105-117.
Z168.29304; M33#5606; R1967,4A144

[7] A new approach to Bernoulli polynomials, Amer. Math. Monthly, 95 (1988), no. 10, 905-911.
Z663.10009; M90c:11014

[8] The sum of like powers of the zeros of the Riemann zeta function, Math. Comp., 50 (1988), no. 181, 265-273.
Z664.10029; M88m:11073; R1988,9A122

LEHMER D.H., LEHMER E., VANDIVER H.S.,
[1] An application of high-speed computing to Fermat's last theorem, Proc. Nat. Acad. Sci. USA, 40 (1954), 25-33.
Z55.04004; M15-778f; R1955,1638

LEHMER E.,
[1] A note on Wilson's quotient, Amer. Math. Monthly, 44 (1937), 237-238.
J63.0106.05

[2] On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson, Ann. Math. (2), 39 (1938), 350-360.
J64.0095.04; Z19.00505

LEHMER E.: see also LEHMER D.H., LEHMER E., VANDIVER H.S.

LE LIDEC P.,
[1] Sur une forme nouvelle des congruences de Kummer-Mirimanoff, C.R. Acad. Sci. Paris, 265 (1967), no. 3, A89-A90.
Z154.29602; M36#108; R1968,5A195

[2] Nouvelle forme des congruences de Kummer-Mirimanoff pour le premier cas du théorème de Fermat, Bull. Soc. Math. France, 97 (1969), 321-328.
Z188.10102; M41#6768; R1970,8A114

LÉMERAY E.M.,
[1] Sur certains nombres analogues aux nombres de Bernoulli, Nouv. Ann. Math. (4), 1 (1901), 509-516.
J32.0283.01

LEMMERMEYER F.,
[1] Reciprocity laws. From Euler to Eisenstein. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2000. xx+487 pp.
Z949.11002; M2001i:11009

LENSE J.,
[1] Über die Nullstellen der Bernoullischen Polynome, Monatsh. Math., 41 (1934), 188-190.
J60.0296.01; Z9.31101

LEOPOLDT H.W.,
[1] Eine Verallgemeinerung der Bernoullischen Zahlen, Abh. Math. Sem. Univ. Hamburg, 22 (1958), 131-140.
Z80.03002; M19-1161e; R1958,9758

[2] Über Klassenzahlprimteiler reeller abelscher Zahlkörper als Primteiler verallgemeinerter Bernoullischer Zahlen, Abh. Math. Sem. Univ. Hamburg, 23 (1959), 36-47.
Z86.03103; M21#1967; R1960,3770

[3] Über Fermatquotienten von Kreiseinheiten und Klassenzahlformeln modulo p, Rend. Circ. Mat., Palermo (2), 9 (1960), 39-50.
Z98.03501; M24#A722; R1961,10A142

[4] Zur Arithmetik in abelschen Zahlkörpern, J. Reine Angew. Math., 209 (1962), 54-71.
Z204.07101; M25#3034; R1963,5A246

[5] Zum wissenschaftlichen Werk von Helmut Hasse, J. Reine Angew. Math., 262/263 (1973), 1-17.
Z268.01011; M58#87; R1974,7A33

[6] Eine p-adische Theorie der Zetawerte, 2: Die p-adische $\Gamma$-Transformation, J. Reine Angew. Math., 274/275 (1975), 224-239.
Z309.12009; M52#351; R1976,1A380

LEOPOLDT H.W.: see also KUBOTA T., LEOPOLDT H.W.

LE PAIGE C.: see le PAIGE C.

LEPKA K.,
[1] Matyás Lerch's work on number theory. Masaryk University, Faculty of Science, Brno, 1995. 78 pp.
Z874.11005; M96g:11003

[2] Historie Fermatovych kvocientu (Fermat - Lerch), Dissertation, Brno, 1998.

LEPOWSKY J.: see DOYON B., LEPOWSKY J., MILAS A.

LERCH M.,
[1] Zur Theorie des Fermatschen Quotienten $\frac{a^{p-1}}{p}=q(a)$, Math. Ann., 60 (1905), 471-490.
J36.0266.03

LETTL G.,
[1] Stickelberger elements and cotangent numbers. Exposition. Math., 10 (1992), no. 2, 171-182.
Z757.11038; M93g:11111; R1993,7A287

LEU MING-GUANG,
[1] Character sums and the series $L(1,\chi)$. J. Aust. Math. Soc. 70 (2001), no. 3, 425-436.
M2002c:11105

LEVINE J.: see CARLITZ L., LEVINE J.

LI JIAN YU: see CHEN JING RUN, LI JIAN YU

LI RONG XIANG: see LIU GUO DONG, LI RONG XIANG

LIBRI G.,
[1] Mémoire sur quelques formules générales d'analyse. J. Reine Angew. Math. 7 (1831), 57-67.

LICHTENBAUM St.,
[1] On p-adic L-fucntions associated to elliptic curves, Invent. Math., 56 (1980), no. 1, 19-55.
Z425.12017; M81j:12013; R1980,5A422

le LIDEC P.: see LE LIDEC P.

LIÉNARD R.,
[1] Tables fondamentales à 50 décimales des sommes $S_n$, $U_n$, ${\Sigma_n$. Centre de Documentation Universitaire, Paris, 1948. 54 pp.
M10-149i

LIGOWSKI W.,
[1] Die Bestimmung der Summe $\Sigma x^r$, Arch. Math. und Phys., 65 (1880), 329-334.
J12.0191.01

LIKHIN V.V.,
[1] Razvitie teorii chisel i funktsij Bernulli v trudakh russkikh i sovetskikh matematikov [Development of the theory of Bernoulli numbers and functions in the works of Russian and Soviet mathematicians]. Dissertatsiya, Moskovsk. Gos. Universitet [Dissertation, Moscow State University], 1954.

[2] Osnovnye etapy razvitiya teorii chisel i funktsij Bernulli [The main stages of development of the theory of numbers and functions of Bernoulli]. Trudy instituta istorii estestvoznaniya i tekhniki Akad. Nauk SSSR 19 (1957), 411-430.
R1961,4A29

[3] Teoriya chisel i funktsij Bernulli i ee razvitie v trudakh otechestvennykh matematikov [The theory of numbers and functions of Bernoulli, and its development in the works of Soviet and Russian mathematicians]. Istoriko-mat. issledovaniya 12 (1959), 59-134.
Z104.29002; M24#A18; R1962,3A22

[4] Ob obobshchennykh chislakh i funktsiyakh Bernulli [On generalized numbers and functions of Bernoulli] (Ukrainian). Nauchn. zap. Poltavsk. pedagogichesk. instituta, fiz.-mat. ser. 13 (1963), no. 2, 3-21.
R1964,6A30

[5] Prilozhenie chisel Bernulli k teorii chisel [Application of Bernoulli numbers in number theory] (Ukrainian). Nauchn. zap. Poltavsk. pedagogichesk. instituta, fiz.-mat. ser. 13 (1963), no. 2, 22-31.
R1964,6A31

LIM PIL-SANG: see KIM HAN SOO, LIM PIL-SANG, KIM TAEKYUN

F.M.S. Lima,
[1] An Euler-type formula for $\beta(2n)$ and closed-form expressions for a class of zeta series,
Integral Transforms Spec. Funct. 23 (2012), no. 9, 649-657.
M2968884

[2] A simpler proof of a Katsurada's theorem and rapidly converging series for $\zeta(2n+1)$ and $\beta(2n)$,
Ann. Mat. Pura Appl. (4) 194 (2015), no. 4, 1015-1024. M3357692

LIN KE-PAO, YAU STEPHEN S.-T.,
[1] Counting the Number of Integral Points in General n-Dimensional Tetrahedra and Bernoulli Polynomials. Canad. Math. Bull. 46 (2003), no. 2, 229-241.
M2004c:11182

LINDELÖF E.,
[1] Le calcul des résidus et ses applications à la théorie des fonctions. Gautier-Villars, Paris, 1905. 141 pp.
J36.0468.01

LIPSCHITZ R.,
[1] Über die Darstellung gewisser Functionen durch die Eulersche Summenformel, J. Reine Angew. Math., 56 (1859), 11-26.

[2] Sur la fonction de Jacob Bernoulli et sur l'interpolation. C. R. Acad. Sci., Paris, 86 (1878), 119-121.
J10.0187.01

[3] Beiträge zu der Kenntniss der Bernouillischen Zahlen, J. Reine Angew. Math., 96 (1884), 1-16.
J16.0152.01

[4] Über Eigenschaften der Bernoullischen Zahlen, Deutsch. Natf. Ber., 1883, 56-57.

[5] Sur la représentation asymptotique de la valeur numérique ou de la partie entière des nombres de Bernoulli, Bull. Sci. Math. (2), 10 (1886), no. 1, 135-144.
J18.0225.01

LIU BO LIAN,
[1] The sum of $k$th powers of the first $n$ integers. Dongbei Shuxue, 6 (1990), no. 3, 291-296.
Z741.11013; M91k:11020

LIU GUO DONG,
[1] $n$-variable Euler numbers and polynomials, and $n$-variable Bernoulli numbers and polynomials. (Chinese), J. Math. (Wuhan) 17 (1997), no. 3, 352-358.
M99k:11031

[2] Higher-order multivariable Euler's polynomial and higher-order multivariable Bernoulli's polynomial, Appl. Math. Mech. (English Ed.) 19 (1998), no. 9, 895-906; translated from Appl. Math. Mech. 19 (1998), no. 9, 827-836 (Chinese).
Z932.11012; M2000c:11028

[3] Generalized Euler-Bernoulli polynomials of order $n$. (Chinese), Math. Practice Theory 29 (1999), no. 3, 5-10.
M2000m:11021

[4] Recurrence sequences and higher order multivariable Euler-Bernoulli polynomials. (Chinese) Numer. Math. J. Chinese Univ. 22 (2000), no. 1, 70-74.
M 2001g:11022

[5] The generalized central factorial numbers and higher order Nörlund Euler-Bernoulli polynomials. (Chinese). Acta Math. Sinica 44 (2001), no. 5, 933-946.
M2002h:11019

[6] Identities and congruences involving higher-order Euler-Bernoulli numbers and polynomials. Fibonacci Quart. 39 (2001), no. 3, 279-284.
Z0992.11021; M2002d:11024

[7] Computational formulas for Euler-Bernoulli polynomials of $n$ variables. (Chinese. English summary) J. Wuhan Univ., Nat. Sci. Ed. 44 (1998), no.5, 554-556.
Z0970.11006

[8] Higher order multivariable Nörlund Euler-Bernoulli polynomials. Appl. Math. Mech. (English Ed.) 23 (2002), no. 11, 1348-1356; translated from Appl. Math. Mech. 23 (2002), no. 11, 1203-1210 (Chinese).
M2004a:33019

[9] Recurrent sequences and higher-order multivariable Euler-Bernoulli polynomials. (Chinese) Xiamen Daxue Xuebao Ziran Kexue Ban 38 (1999), no. 3, 352-356.

[10] Generalizations of Vassilev's formula. (Chinese. English summary) Gongcheng Shuxue Xuebao 19 (2002), no. 4, 95-100.

[11] Solution of a problem for Euler numbers. (Chinese) Acta Math. Sinica 47 (2004), no. 4, 825-828.
Z1016.11009; M2003k:11031

[12] Degenerate Bernoulli numbers and polynomials of higher order. (Chinese). J. Math. (Wuhan) 25 (2005), no. 3, 283-288.
M2006a:05007

[13] On congruences of Euler numbers modulo an odd square. Fibonacci Quart. 43 (2005), no. 2, 132-136.
M2006a:11021

[14] Congruences for higher-order Euler numbers. Proc. Japan Acad. Ser. A Math. Sci. 82 (2006), no. 3, 30-33.
M2006m:11025

LIU GUO DONG, LI RONG XIANG,
[1] Sums of products of Euler-Bernoulli-Genocchi numbers. (Chinese) J. Math. Res. Exposition 22 (2002), no. 3, 469-475.
M2003f:11028

Liu, Guodong; Luo, Hui,
[1] Some identities involving Bernoulli numbers. Fibonacci Quart. 43 (2005), no. 3, 208-212.
M2006h:11021

LIU HUANING, ZHANG WENPENG,
[1] On the hybrid mean value of Gauss sums and generalized Bernoulli numbers. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 6, 113-115.
R05.06-13A153

LIU JIAN JUN,
[1] A kind of counting identities containing Bernoulli numbers. (Chinese) J. Liaoning Univ. Nat. Sci. 29 (2002), no. 4, 301-303.

LIU MAI XUE, ZHANG ZHI ZHENG,
[1] A class of computational formulas involving the multiple sum on Genocchi numbers and the Riemann zeta function. (Chinese) J. Math. Res. Exposition 21 (2001), no. 3, 455-458.
M2002j:11158

LIU TONG,
[1] The Ankeny-Artin-Chowla formula over sextic cyclic number fields. (Chinese) Kexue Tongbao (Chinese) 43 (1998), no. 5, 471-474.

[2] Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields. Chinese Sci. Bull. 43 (1998), no. 10, 824-826.
Z1017.11053; M99k:11175

LJUNGGREN W.,
[1] Aritmetiske egenskaper ved de Bernoulliske tall [Arithmetical properties of the Bernoulli numbers], Norsk Mat. Tidsskr., 28 (1946), 33-37.
Z60.08701; M8-314f

[2] A theorem on the elementary symmetric functions of the n first odd numbers, Norske Vid. Selsk. Forh., 19 (1946), no. 5, 14-17.
Z60.08508; M8-368g

[3] Sur un théorème de M. E. Jacobsthal, Avhdl. Norske Vid. Akad. Oslo, 1 (1947), no. 5, 1-14.
Z30.19802; M9-568e

LOBACHEVSKII N.I.,
[1] Sposob uverit'sya v ischeznovenii strok i priblizhat'sya k znacheniyu funktsij ot ves'ma bol'shikh chisel [A method of convincing oneself of the vanishing of series and approximating the value of functions from very large numbers]. (1835). Sobranie sochinenij [Collected Works], Vol. 5, Moskva, 1951, 81-162.
M13-612n

LOEB D.E.,
[1] The iterated logarithmic algebra, Adv. Math., 86 (1991), no. 2, 155-234.
Z816.05011; M92g:05022

[2] The iterated logarithmic algebra. II. Sheffer sequences. J. Math. Anal. Appl., 156 (1991), no. 1, 172-183.
Z742.05010; M92d:05013

LOEB D.E.: see also DI BUCCHIANICO A., LOEB D.

LOEB D.E.: see also DI BUCCHIANICO A., LOEB D., ROTA G.-C.

LÖH G.: see KELLER W., LÖH G.

LOHNE J.,
[1] Potenssummer av de naturlige tall [Sums of powers of natural numbers], Nordisk Mat. Tidsskrift, 6 (1958), 155-158, 182.

LONGCHAMPS G.,
[1] Sur les nombres de Bernoulli, Ann. de l'Ecole Normale (2), 8 (1879), 55-80.
J11.0185.01

LÓPEZ J.L.; TEMME N.M.,
[1] Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions. Stud. Appl. Math. 103 (1999), no. 3, 241-258.
M2000f:41004

[2] Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials, J. Math. Anal. Appl. 239 (1999), no. 2, 457-477.
M2000k:33019

LORENZUTTA S.: see DATTOLI G., LORENZUTTA S., CESARANO C.

LOUBOUTIN ST.,
[1] Détermination des corps quartiques cycliques totalement imaginaires à groupe des classes d'idéaux d'exposant $\leq 2$. Manuscr. Math., 77 (1992), no. 4, 385-404.
Z799.11046; M93m:11114

[2] Computation of relative class numbers of imaginary abelian number fields, Experiment. Math. 7 (1998), no. 4, 293-303.
Z0929.11065; M2000c:11207

LOVELACE, Augusta Ada, Countess of: see KING, AUGUSTA ADA

LU HONG-WEN,
[1] Congruences for the class number of quadratic fields, Abh. Math. Sem. Univ. Hamburg, 52 (1982), 254-258.
Z495.12003; M85b:11096; R1983,12A393

LUCAS E.,
[1] De quelques nouvelles formules de sommation. Nouv. Ann. Math. (2), 14 (1875), 487-494. J07.0126.01

[2] Théorie nouvelle des nombres de Bernoulli et d'Euler, C.R. Acad. Sci. Paris, 83 (1876), 539-541.
J08.0143.01

[3] Sur les rapports qui existent entre le triangle arithmétique de Pascal et les nombres de Bernoulli, Nouv. Ann. Math. (2), 15 (1876), 497-499.
J08.0143.02

[4] Théorie nouvelle des nombres de Bernoulli et d'Euler, Annali di Math., Milano (2), 8 (1877), 56-79.
J09.0186.01

[5] Sur les théorèmes de Binet et de Staudt concernant les nombres de Bernoulli, Nouv. Ann. Math. (2), 16 (1877), 157-160.
J09.0187.01

[6] Sur la généralisation de deux théorèmes dus à MM. Hermite et Catalan, Nouv. Corres. Math., 3 (1877), 69-73.
J09.0188.01

[7] On the development of $\bigl({z\over{1-e^{-z}}}\bigr)^{\alpha}$ in a series, Messeng. Math. (2), 7 (1877), 82-84.
J09.0188.02

[8] Sur les sommes des puissances semblables des nombres entries. Nouv. Ann. (2) 16 (1877), 18-26.
J09.0113.01

[9] Recherches sur plusieurs ouvrages de Léonard de Pise et sur diverses questions d'arithmétique supérieure. Boncompagni Bull. 10 (1877), 129-193, 239-293.
J09.0111.02

[10] On the successive summations of $1^m + \cdots +x^m$, Messeng. Math., 7 (1878), 84-86.
J09.0177.01

[11] On development in series, Messeng. Math., 7 (1877), 116.
J09.0314.02

[12] On Eulerian numbers, Messeng. Math., 7 (1877), 139-141.
J10.0191.02

[13] Sur les congruences des nombres eulériens et les coefficients différentiels des fonctions trigonométriques, suivant un module premier, Bull. Soc. Math. France, 6 (1878), 49-54.
J10.0139.04

[14] Sur les développements en séries, Bull. Soc. Math. France, 6 (1878), 57-68.
J10.0191.01

[15] Sur les nouvelles formules de MM. Seidel et Stern, concernant les nombres de Bernoulli, Bull. Soc. Math. France, 8 (1880), 169-173.
J12.0194.03

[16] Démonstration du théorème de Clausen et de Staudt concernant les nombres de Bernoulli, Mathesis, 3 (1883), 25-28.
J15.0205.01

[17] Démonstration du théorème de Clausen et de Staudt, sur les nombres de Bernoulli, Bull. Soc. Math. France, 11 (1883), 69-72.
J15.0205.01

[18] Théorie des nombres, Paris, (1891), t.1.
J23.0174.02

[19] Sur les théorèmes énoncés par Fermat, Euler, Wilson, Staudt et Clausen, Mathesis (2), 1 (1891), 5-12.
J23.0197.02

LUCAS E., CATALAN E.,
[1] Sur les calcul symbolique des nombres de Bernoulli, Nouv. Corres. Math., 2 (1876), 328-338.
J08.0150.05

LUCHT L.G.,
[1] Arithmetical aspects of certain functional equations, Acta Arith. 82 (1997), no. 3, 257-277.
Z980.02698

LUCK J.-M.: see WALDSCHMIDT M. et al.

LUNDELL A.T.,
[1] On the denominator of generalized Bernoulli numbers, J. Number Theory, 26 (1987), 79-88.
Z621.10010; M88d:11020; R1987,10A64

Luo, Hui; Liu, Guo Dong,
[1] Congruences for higher-order Euler numbers. (Chinese) Pure Appl. Math. (Xi'an) 21 (2005), no. 4, 345-348.
M2006m:11026

LUO QIU MING,
[1] Generalizations of Bernoulli numbers and higher-order Bernoulli numbers. (Chinese) Pure Appl. Math. 18 (2002), no. 4, 305-308.
M2003m:11036

[2] The relations of Bernoulli polynomials and Euler polynomials. (Chinese) Math. Practice Theory 33 (2003), no. 3, 119-122.

[3] Euler polynomials of higher order involving the stirling numbers of the second kind. Austral. Math. Soc. Gaz. 31 (2004), no. 3, 194-196.

[4] Some recursion formulae and relations for Bernoulli numbers and Euler numbers of higher order. Adv. Stud. Contemp. Math. (Kyungshang) 10 (2005), no. 1, 63-70.
M2005h:11039

[5] On the Apostol-Bernoulli polynomials. Cent. Eur. J. Math. 2 (2004), no. 4, 509-515 (electronic).
M2005m:11031

[6] An explicit formula for the Euler numbers of higher order. Tamkang J. Math. 36 (2005), no. 4, 315-317.

[7] An explicit formula for the Euler polynomials. Integral Transforms Spec. Funct. 17 (2006), no. 6, 451-454.

[8] Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. Taiwanese J. Math. 10 (2006), no. 4, 917-925.
M2007c:33005

Luo, Qiu Min; Li, Chang Qing,
[1] Generalizations of the Euler numbers of higher order and their applications. (Chinese) Pure Appl. Math. (Xi'an) 21 (2005), no. 4, 325-328, 334.
M2006m:11027

LUO QIU MING, AN CHUN XIANG,
[1] Relations between Bernoulli numbers of higher order and Euler numbers of higher order. (Chinese) J. Henan Norm. Univ. Nat. Sci. 32 (2004), no. 2, 28-30, 37.

LUO QIU-MING, GUO TIAN FEN, QI FENG,
[1] Relations of Bernoulli numbers and Euler numbers. (Chinese) J. Henan Norm. Univ. Nat. Sci. 31 (2003), no. 2, 9-11.

LUO QIU-MING, GUO BAI-NI, QI FENG, DEBNATH L.,
[1] Generalizations of Bernoulli numbers and polynomials. Int. J. Math. Math. Sci. 2003, no. 59, 3769-3776.
M2004m:11022

Luo, Qiu Ming; Liu, Ai Qi,
[1] Generalizations of higher-order Euler polynomials and their applications. (Chinese) J. Math. (Wuhan) 26 (2006), no. 5, 574-578.

Luo, Qiu Ming; Ma, Yun Xin; Qi, Feng,
[1] Relations between higher-order Bernoulli polynomials and higher-order Euler polynomials. (Chinese) J. Math. (Wuhan) 25 (2005), no. 6, 631--636.

LUO QIU-MING, QI FENG,
[1] Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials. Adv. Stud. Contemp. Math. (Kyungshang) 7 (2003), no. 1, 11-18.

[2] Generalizations of Euler numbers and Euler numbers of higher order. Chinese Quart. J. Math. 20 (2005), no. 1, 54-58.
M2006e:11025

LUO QIU-MING, QI FENG, DEBNATH L.,
[1] Generalizations of Euler numbers and polynomials. Int. J. Math. Math. Sci. 2003, no. 61, 3893-3901.
M2004k:11019

Luo, Qiu-Ming; Srivastava, H. M.,
[1] Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials. J. Math. Anal. Appl. 308 (2005), no. 1, 290-302.
M2006e:33012

^M [2] Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials. Comput. Math. Appl. 51 (2006), no. 3-4, 631--642.
M2006k:42050

^M LUO QIU-MING: see also ZHENG YU MIN, LUO QIU MING

LURSMANASHVILI A.P.,
[1] On the number of lattice points in multidimensional spheres. (Russian) Akad. Nauk. Gruzin. SSR. Trudy Tbiliss. Mat. Inst. Razmadze, 19 (1953), 79-120.
Z52.04202; M16-451b; R1954,3210

LYAKHOVITSKII V.N.,
[1] On a relationship for Bernoulli numbers. (Russian) Mat. Zametki, 1 (1967), 633-644.
English translation: Math. Notes of the Acad. of Sci. USSR, 1 (1967), 420-427
Z174.07402; M35#6613; R1967,11V243

LYCHE R.T.: see TAMBS LYCHE R.


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