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FAIRLIE D.B., VESELOV A.P.,
[1] Faulhaber and Bernoulli polynomials and solitons. Advances in nonlinear mathematics and science. Phys. D 152/153 (2001), 47-50.
M2002d:37121

FANG C.-H., EIE M.,
[1] On the values of a zeta function at non-positive integers, Pacific J. Math., 145 (1990), no. 2, 201-210.
Z733.11031; M92d:11034; R1991,6A78

FANG JIAN PING: see ZHANG JING, FANG JIAN PING

FEINLER F.J.,
[1] A new method for calculating the Bernoulli numbers, Mess. Math., 55 (1925), 40-44.
J51.0077.01

[2] Recurrence formulas for the Bernoulli numbers derived from zero differences (Abstract), Bull. Amer. Math. Soc., 32 (1926), 126.
J52.0361.12

[3] A reduced Bernoulli polynomial and its properties (Abstract). Bull. Amer. Math. Soc., 34 (1928), 698.
J54.0129.11

FENDER W.,
[1] Zur Theorie von verallgemeinerten Bernoullischen und Eulerschen Zahlen, Dissertation, Universität Jena, (1911), 58p.
J42.0458.04

FENG KE QIN,
[1] The Ankeny-Artin-Chowla formula for cubic number field (Chinese, English summary), J. China Univ. Sci. Tech., 12 (1982), no. 1, 20-27.
M85a:11018

[2] A note on irregular prime polynomials in cyclotomic functional field theory, J. Number Theory, 22 (1986), no.2, 240-245.
Z578.12012; M87g:11156; R1986,8A325

FENG KE QIN, GAO W.Y.,
[1] Bernoulli-Goss polynomial and class number of cyclotomic function fields, Sci. China Ser. A, 33 (1990), no. 6, 654-662.
Z708.11064; M91m:11099

FERGOLA E.,
[1] Sopra la sviluppo della funzione $1\over{ce^x-1$ e sopra una nuovo expressione dei numeri di Bernoulli, Mem. Accad. Sci., Napola, 2, (1855/57), 315-324.

FERGUSON H.R.P.,
[1] Bernoulli numbers and non-standard differentiable structures on $(4k-1$)-spheres, Fibonacci Quart., 11 (1973), no. 1, 1-14.
Z225.10012; M46#7134; R1973,9A537

FERRERO B.,
[1] Iwasawa invariants of abelian number fields, Thesis, Princeton Univ., 1975.

[2] An explicit bound for Iwasawa's $\lambda$-invariant, Acta Arith., 33 (1977), no. 4, 405-408.
Z323.12004; M56#15605; R1978,7A460

FERRERO B., GREENBERG R.,
[1] On the behaviour of p-adic L-functions at $s=0$, Invent. Math., 50 (1978), no. 1, 91-102.
Z441.12003; M80f:12016; R1979,7A402

FERRERO B., WASHINGTON L.C.,
[1] The Iwasawa invariant $\mu_p$ vanishes for abelian number fields, Ann. of Math. (2), 109 (1979), no. 2, 377-395.
Z443.12001; M81a:12005; R1979,12A379

FIELDS J.C.,
[1] Related expressions for Bernoulli's and Euler's numbers, Amer. J. Math., 13 (1891), 191-192.
J22.0266.03

FIKHTENGOLTS G.M.,
[1] Kurs differentsial'nogo i integral'nogo ischisleniya [A course in differential and integral calculus], Vol. 2, Ch. 12. Moscow, 1948.
Z33.10703

FILASETA M.: see ADELBERG A., FILASETA M.

FILLEBROWN S.,
[1] Faster computation of Bernoulli numbers, J. Algorithms, 13 (1992), no. 3, 431-445.
Z755.11006; M94d:68044

FLAJOLET P.,
[1] On congruences and continued fractions for some classical combinatorial quantities, Discrete Math., 41 (1982), no. 2, 145-153.
M84f:05005; R1983,2A58

FLAJOLET P., PRODINGER H.,
[1] On Stirling numbers for complex arguments and Hankel contours. SIAM J. Discrete Math. 12 (1999), no. 2, 155-159.
R921.05001

FLAJOLET P.: see DUMAS P., FLAJOLET P.

FLETCHER A., MILLER J.C.P., ROSENHEAD L., COMRIE L.J.,
[1] An Index of Mathematical Tables, Vol. I, II, 2nd ed. Addison Wesley Publ. Co., Inc., Reading, Mass., 1962. xi + pp. 1-608; iv + pp. 609-994.
M26#365a,b; R1963,7V44K

FLOCKE S.: see BUTZER P.L., FLOCKE S., HAUSS M.

FOATA D.,
[1] Propriétés arithmétiques des polynômes d'Euler. Séminaire Delange-Pisot-Poitou, No. 20 (1967/68).
Z272.05006; R1969,9A79

[2] Groupes de réarrangements et nombres d'Euler, C.R. Acad. Sci. Paris Sér. A, 275 (1972), 1147-1150.
Z269.20006; M47#8320; R1973,11V421

[3] Réarrangements d'applications associées aux nombres de Genocchi, C. R. des Journées Mathématiques de la Société Math. de France, pp. 113-121. Cahiers Math. Montpellier, no. 3, U. E. R. de Math., Univ. Sci. Tech. Languedoc, Montpellier, 1974.
M51#12542

[4] Further divisibility properties of the $q$-tangent numbers. Proc. Amer. Math. Soc. 81 (1981), no. 1, 143--148.
M81k:05005

FOATA D., SCHÜTZENBERGER M.-P.,
[1] Théorie Géométrique des Polynômes Eulériens. Lecture Notes in Mathematics, No. 138. Springer-Verlag, Berlin-Heidelberg- New York, 1970.
Z214.26202; M42#7523; R1971,1V267

[2] Nombres d'Euler et permutations alternantes. In: A Survey of Combinatorial Theory, 173-187. North-Holland, Amsterdam, 1973.
Z271.05005; M50#6870; R1974,4V272

FOATA D., STREHL V.,
[1] Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers, Math. Z., 137 (1974), 257-264.
Z274.05007; M50#450; R1975,3V447

[2] Euler numbers and variations of permutations, Colloquio Internazionale sulle Teorie Combinatorie (Roma, 1973), Tomo I, 119-131. Atti dei Convegni Lincei, No. 17, Accad. Naz. Lincei, Roma, 1976.
Z361.05010; M55#7795

FOATA D.: see also ANDREWS G., FOATA D.

FOATA D.: see also DUMONT D., FOATA D.

FORDER H.G.,
[1] Euler numbers, Math. Gazette, 14 (1928/29), 233.
J54.0182.01

FORRESTER P.J.,
[1] Extensions of several summation formulae of Ramanujan using the calculus of residues, Rocky Mountain J. Math., 13 (1983), no. 4, 557-572.
Z537.10007; M85i:40004

FORT T.,
[1] Generalizations of the Bernoulli polynomials and numbers and corresponding summation formulas, Bull. Amer. Math. Soc., 48 (1942), no. 8, 567-574.
Z61.19807; M4-79f

[2] An addition to "Generalizations of the Bernoulli polynomials and numbers and corresponding summation formulas", Bull. Amer. Math. Soc., 48 (1942), 949.
Z61.19901; M4-79g

FOUCHÉ W.,
[1] A reciprocity law for polynomials with Bernoulli coefficients, Trans. Amer. Math. Soc., 288 (1985), no. 1, 59-67.
Z558.10013; M86d:11085; R1986,1A387

[2] On the p-adic zeros of polynomials with Bernoulli coefficients, Arch. Math., 45 (1985), no. 6, 534-537.
Z563.10013; M87b:11019; R1986,6A193

[3] On the Kummer-Mirimanoff congruences, Quart. J. Math. (Oxford)(2), 37 (1986), no. 147, 257-261.
Z604.10007; M88a:11022; R1987,12A73

[4] The distribution of Bernoulli numbers modulo primes, Arch. Math., 50 (1988), no. 2, 139-144.
Z644.10011; M89d:11011; R1988,8A101

FOULKES H.O.,
[1] Tangent and secant numbers and representations of symmetric groups, Discrete Math., 15 (1976), no. 4, 311-324.
M53#10596; R1976/77,2V444

FOX, G.J.,
[1] A $p$-adic $L$-function of two variables, Ph.D. thesis, University of Georgia, Athens, Georgia, 1997, 156pp.

[2] Euler polynomials at rational numbers, C. R. Math. Acad. Sci. Soc. R. Can. 21 (1999), no. 3, 87-90.
Z939.11013; M2000f:11021

[3] Congruences relating rational values of Bernoulli and Euler polynomials. Fibonacci Quart. 39 (2001), no. 1, 50-57.
M2002a:11014

[4] A $p$-adic $L$-function of two variables. Enseign. Math. (2) 46 (2000), no. 3-4, 225-278.

M2002c:11162

[5] Kummer congruences for expressions involving generalized Bernoulli polynomials. J. Théor. Nombres Bordeaux 14 (2002), no. 1, 187-204.
Z1022.11008; M2003i:11030

[6] A method of Washington applied to the derivation of a two-variable $p$-adic $L$-function. Pacific J. Math. 209 (2003), no. 1, 31-40.

FOX G.J., URBANOWICZ J., WILLIAMS K.S.,
[1] Gauss' congruence from Dirichlet's class number formula and generalizations. Number theory in progress, Vol. 2 (Zakopane, 1997), 813-839, de Gruyter, Berlin, 1999.
Z929.11010; M2000f:11146

FRAENKEL A.S.,
[1] A characterization of exactly covering congruences, Discrete Math., 4 (1973), no. 4, 359-366.
Z257.10003; M47#4906; R1973,11A101

[2] Further characterizations and properties of exactly covering congruences, Discrete Math., 12 (1975), no. 1, 93-100.
Z306.10002; M51#10276; R1975,11V357

FRAME J.S.,
[1] Euler and tangent numbers and the exponential shift, Amer. Math. Monthly, 67 (1960), 1016-1019.
R1961,10A151

[2] Bernoulli numbers modulo 27000, Amer. Math. Monthly, 68 (1961), 87-95.
Z134.27401; M23#A1586; R1962,1A146

[3] The Hankel power sum matrix inverse and the Bernoulli continued fraction, Math. Comp., 33 (1979), no. 146, 815-826.
Z419.65029; M80f:65044; R1980,1A406

[4] Primes, ratios, and Bernoulli numbers (problem), Amer. Math. Monthly, 90 (1983), no. 9, 645-646.

[5] More like $\zeta(2[n/2])$ than $\zeta(2n)$ (problem), Amer. Math. Monthly, 93 (1986), 744-745.

FRANÇON J., VIENNOT G.,
[1] Permutations selon leurs pics, creux, doubles montées et doubles descentes, nombres d'Euler et nombres de Genocchi, Discrete Math., 28 (1979), no. 1, 21-35.
Z409.05003; M81a:05002; R1980,5V425

FRANSÉN A.,
[1] Properties of Stirling polynomials and a disproof of Robertson's conjecture, J. Math. Anal. Appl., 154 (1991), no. 2, 446-451.
Z729.30002; M92d:11016

FRAPPIER C.,
[1] Representation formulas for entire functions of exponential type and generalized Bernoulli polynomials, J. Austral. Math. Soc. Ser. A, 64 (1998), no. 3, 307-316.
Z909.30018; M99i:30045; R1999,1B19

[2] Generalised Bernoulli polynomials and series. Bull. Austral. Math. Soc. 61 (2000), no. 2, 289-304.
Z0981.11008; M2001h:33009

[3] A unified calculus using the generalized Bernoulli polynomials. J. Approx. Theory 109 (2001), no. 2, 279-313.
Z0976.41029; M2002e:30003

FRESNEL J.,
[1] Congruences entre les nombres de Bernoulli, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 6 (1964/65), (1967), no. 14, 1-12.
Z206.33601; M35#6505; R1968,5A206

[2] Nombres de Bernoulli et fonctions L p-adiques, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 7 (1965/66), (1967), no. 14, 1-15.
Z247.12013; M35#6507; R1968,5A189

[3] Les fonctions p-adiques L de Dirichlet, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 7 (1965/66), (1967), no. 17, 1-8.
Z222.12017; M35#6505; R1968,5A190

[4] Nombres de Bernoulli généralisés et fonctions L p-adiques, C.R. Acad. Sci., Paris, 263 (1966), 337-340.
Z147.02205; M34#1304; R1968,4V272

[5] Applications arithmétiques de la formule p-adique des résidus, Sémin. théor. nombres Delange-Pisot-Poitou, Fac. Sci., Paris, 8 (1966/67), (1968), no. 18, 1-8.
Z162.07003; R1969,3A277

[6] Nombres de Bernoulli et fonctions L p-adiques, Ann. Inst. Fourier, 17 (1967), (1968), 281-333.
Z157.10302; M37#169; R1968,9A121

[7] Fonctions zêta p-adiques des corps de nombres abéliens réels, Bull. Soc. Math. France, Mém. No. 25, 1971, pp. 83-89.
Z242.12009; M52#3121; R1972,3A321

FRESNEL J.: see also AMICE Y., FRESNEL J.

FRICKE A.,
[1] Die Potenzsummenformel und ihre Struktur, Prax. Math., 29 (1987), no. 8, 462-470.
M89k:40008; R1988,7A103

FRIEDMAN E.C.,
[1] Ideal class group in basic $ Z_{p_1 \times \cdots \times Z_{p_t}$-extension of abelian number fields, Invent. Math., 65 (1982), no. 3, 425-440.
Z495.12007; M83i:12007; R1982,6A322

FRIEDMAN E., SANDS J. W.,
[1] On the $l$-adic Iwasawa $\lambda$-invariant in a $p$-extension. With an appendix by Lawrence C. Washington. Math. Comp. 64 (1995), no. 212, 1659-1674.
Z854.11055; M96a:11116; R1996,4A268

FRIEDMANN A.A., TAMARKINE J.,
[1] Sur les congruences du second degré et les nombres de Bernoulli, Math. Ann., 62 (1906), no. 3, 409-412.
J37.0228.02

[2] Quelques formules concernant la théorie de la fonction $[x]$ et des nombres de Bernoulli, J. Reine Angew. Math., 135 (1908), 146-156.
J39.0262.10

FROBENIUS G.,
[1] Über den Fermatschen Satz, Sitzungsber. Preuss. Akad. Wiss. Berlin (1909), 1222-1224. = J. Reine Angew. Math., 137 (1910), 314-316. = Gesammelte Abhandlungen, Springer, Berlin, Bd. 3, 1968, 428-430.
J41.0236.02

[2] Über den Fermatschen Satz, II, Sitzungsber. Preuss. Akad. Wiss. Berlin, (1910), 200-208. = Gesammelte Abhandlungen, Springer, Berlin, Bd. 3, 1968, 431-439.
J41.0236.04

[3] Über die Bernoullischen Zahlen und die Eulerschen Polynome, Sitzungsber. Preuss. Akad. Wiss., (1910), no. 2, 809-847; Ges. Abhandlungen, Berlin: Springer, Bd. 3, 1968, 440-478.

[4] Über den Fermatschen Satz, III, Sitzungsber. Preuss. Akad. Wiss., (1914), N 22, 653-681; Ges. Abhandlungen, Berlin e.a.: Springer, Bd. 3, 1968, 648-676.
J45.0290.01

FUCHS P.,
[1] Bernoulli numbers and binary trees. Tatra Mt. Math. Publ. 20 (2000), 111-117.
M2002e:11018; R02.03-13A.99

FUETER R.,
[1] Kummers Kriterium zum letzten Theorem von Fermat, Math. Ann., 85 (1922), 11-20.
J48.0130.05

FUJII A.,
[1] Some problems of Diophantine approximation in the theory of the Riemann zeta function. Proc. Japan Acad. Ser. A Math. Sci., 68 (1992), no. 6, 131-136.
Z795.11034; M93g:11093

[2] Some problems of Diophantine approximation in the theory of the Riemann zeta function. II. Proc. Japan Acad. Ser. A Math. Sci., 69 (1993), no. 4, 85-90.
Z804.11049; M94b:11084

[3] Some problems of Diophantine approximation in the theory of the Riemann zeta function. III. Comment. Math. Univ. St. Paul., 42 (1993), no. 2, 161-187.
Z805.11058; M94i:11065

[4] On the zeros of the Epstein zeta functions, J. Math. Kyoto Univ. 36 (1996), no. 4, 697--770.
Z970.52672; M98e:11049

FUJISAKI G.,
[1] A generalization of Carlitz's determinant, Sci. Pap. College Arts Sci. Univ. Tokoyo, 40 (1991), no. 2, 63-68.
Z722.11014; M91m:11012; R191,10A220

FUJIWARA M.,
[1] Sur les nouveaux nombres de M. Pascal, Rom. Acc. L. Rend. (5), 17 (1908), 401-405.
J39.0264.01

FUKUHARA S.,
[1] The space of period polynomials, Acta Arith. 82 (1997), no. 1, 77-93.
Z881.11046; M99i:11027

[2] Generalized Dedekind symbols associated with the Eisenstein series. Proc. Amer. Math. Soc. 127 (1999), no. 9, 2561-2568.
Z924.11030; M2000a:11061

FUNG. G., GRANVILLE A., WILLIAMS H.C.,
[1] Computation of the first factor of the class number of cyclotomic fields, J. Number Theory, 42 (1992), no. 3, 297-312.
Z762.11039; M93k:11097

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