Karl Dilcher's Publications

Refereed journal publications:

1. The Maximum modulus of zeros of polynomials,
C. R. Math. Rep. Acad.Sci. Canada 5 (1983), 189-194. MR 85a:30014.

2. Zero-free regions for Bernoulli polynomials,
C. R. Math. Rep. Acad. Sci.Canada 5 (1983), 241-246. MR 85a:30015.

3. Irreducibility and zeros of generalized Bernoulli polynomials,
C. R. Math. Rep. Acad. Sci. Canada 6 (1984), 273-278. MR 85k:11010.

4. On a diophantine equation involving quadratic characters,
Compositio Math. 57 (1986), 383-403. MR 87e:11046.

5. A generalization of the Eneström-Kakeya theorem,
J. Math. Anal. Appl. 116 (1986), 473-488. MR 87j:30011.

6. Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials,
J. Approx. Theory 49 (1987), 321-330. MR 88g:33001.

7. Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters,
J. Number Theory 25 (1987), 72-80. MR 88a:11021.

8. A generalization of Fibonacci polynomials and a representation of Gegenbauer polynomials of integer order,
Fibonacci Quart. 25 (1987), 300-303. MR 88i:33012.

9. Polynomials related to expansions of certain rational functions in two variables,
SIAM J. Math. Anal. 19 (1988), 473-483. MR 89d:33015.

10. Zeros of Bernoulli, generalized Bernoulli, and Euler polynomials,
Memoirs of the Amer. Math. Soc., No. 386, 1988, 97pp. MR 89h:30005.

11. (With K.B. Stolarsky) Zeros of certain rational approximations to the cosecant,
J. Math. Anal. Appl. 143 (1989), MR 90j:30009. 109-125.

12. (With J.M. Borwein and P.B. Borwein) Pi, Euler numbers and asymptotic expansions,
Amer. Math. Monthly 96 (1989), 681-687. MR 91c:40002.

13. Multiplikationstheoreme für die Bernoullischen Polynome und explizite Darstellungen der Bernoullischen Zahlen [Multiplication theorems for Bernoulli polynomials and explicit representations for Bernoulli numbers],
Abh. Math. Sem. Univ. Hamburg 59 (1989), 143-156. MR 91h:11012.

14. Real Wronskian zeros of polynomials with nonreal zeros,
J. Math. Anal. Appl. 154 (1991), 164-183. MR 92c:30005.

15. Zeros of certain cyclotomy-generated polynomials,
Fibonacci Quart. 29 (1991), 150-156. MR 92g:12002.

16. (With K.B. Stolarsky) Zeros of the Wronskian of a polynomial,
J. Math. Anal. Appl. 162 (1991), 430-451. MR 92m:30008.

17. (With J.D. Nulton and K.B. Stolarsky) The zeros of a certain family of trinomials,
Glasgow Math. J. 34 (1992), 55-74. MR 93b:26022.

18. (With K.B. Stolarsky) Sequences of polynomials whose zeros lie on fixed lemniscates,
Periodica Math. Hung. 25 (1992), 179-190. MR 94b:30009.

19. (With K.B. Stolarsky) On a class of nonlinear differential operators acting on polynomials,
J. Math. Anal. Appl. 170 (1992), 382-400. MR 94b:34116.

20. Generalized Euler constants for arithmetical progressions,
Math. Comp. 59 (1992), 259-282. MR 92k:11145.

21. (With K.B. Stolarsky) Zeros of the Wronskian of Chebyshev and ultraspherical polynomials,
Rocky Mountain J. Math. 23 (1993), 49-65. MR 94e:33009.

22. An inequality for sections of certain power series,
Arch. Math. 60 (1993), 339-344. MR 94a:26042.

23. On a class of iterative recurrence relations,
Proceedings of the 5th Internat. Conf. on Fibonacci Numbers and Their Applications (St. Andrews, Scotland, July 1992), 143-158. Kluwer Acad. Publ., Dordrecht, 1993. MR 95b:11015.

24. On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function,
Aequationes Math. 48 (1994), 55-85. MR 95h:11086.

25. (With P.B. Borwein and Weiyu Chen) Zeros of iterated integrals of polynomials,
Canad. J. Math. 47 (1995), 65-87. MR 96b:30010.

26. (With L. Skula) A new criterion for the first case of Fermat's last theorem,
Math. Comp. 64 (1995), 363-392. MR 95c:11034.

27. Some q-series identities related to divisor functions,
Discrete Math. 145 (1995), 83-93. MR 96i:11020.

28. (With L.A. Rubel) Zeros of sections of divergent power series,
J. Math. Anal. Appl. 198 (1996), 98-110. MR 96m:30002.

29. Sums of products of Bernoulli numbers,
J. Number Theory 60 (1996), 23-41. MR 97h:11014.

30. (With R. Crandall and C. Pomerance) A search for Wieferich and Wilson primes,
Math. Comp. 66 (1997), 433-449. MR 97c:11004.

31. (With T. Agoh and L. Skula) Fermat quotients for composite moduli,
J. Number Theory 66 (1997), 29-50. MR 98h:11002.

32. (With T. Agoh and L. Skula) Wilson quotients for composite moduli,
Math. Comp. 67 (1998), 843-861. MR 98h:11003.

33. (With J.I. Brown and R.J. Nowakowski) Roots of independence polynomials of well covered graphs.
J. Algebraic Combin. 11 (2000), no. 3, 197-210.

34. (With R.P. Brent, R.E. Crandall and C. van Halewyn) Three new factors of Fermat numbers,
Math. Comp. 69 (2000), no. 231, 1297-1304. MR 2000j:11194.

35. Hypergeometric functions and Fibonacci numbers,
Fibonacci Quart. 38 (2000), no. 4, 342-363.

36. (With K. Haller) Multiple zeta sums via box splines,
Proc. of the Turku Colloquium on Number Theory (to appear, 2001).

37. An extension of Fermat's little theorem, and congruences for Stirling numbers,
Amer. Math. Monthly 107 (2000), no. 10.

38. Nested squares and evaluations of integer products,
Experiment. Math. 9 (2000), no. 3, 369-372.

39. Bernoulli Numbers and Confluent Hypergeometric Functions,
Proceedings of the Millennial Conference on Number Theory, Univ. of Illinois, May 2000 (to appear).

Unrefereed publications:

(With J.M. Borwein and P.B. Borwein) Boole summation and asymptotic expansions of some special series,
Conference Report of the 9th Czechoslovak Colloquium on Number Theory, Ra\v{ckova Dolina, Sept. 1989, Masaryk University, Brno, 1990, 11-18.

Other publications:

(With L. Skula and I.Sh. Slavutskii) Bernoulli Numbers. Bibliography (1713-1990).
Queen's Papers in Pure and Applied Mathematics, No. 87, Queen's University, Kingston, Ontario, 1991. iv+175pp. MR 92f:11001.

(With N.D. Anderson and J. Rovnyak) Mathematics Research Libraries at the End of the Twentieth Century,
Notices Amer. Math. Soc. 44 (1997), no. 11, 1469-1472. Reprinted in: Canadian Math. Soc. Notes 29 (1997), no. 8, 44-47.

Encyclopedia article:

The von Staudt-Clausen theorem.
In ``Encyclopedia of Mathematics, Supplement II", 484-485. Kluwer Academic Publ., 2000.

Proceedings edited:

Number Theory. Fourth Conference of the Canadian Number Theory Association (Halifax, Nova Scotia, July 2-8, 1994). CMS Conference Proceedings, Vol. 15, Amer. Math. Soc., Providence, R.I., 1995. MR 96c:11003.


Jirí Herman, Radan Kucera and Jaromír Simsa:
Equations and Inequalities. Elementary Problems and Theorems in Algebra and Number Theory
Springer-Verlag, New York, to appear in April, 2000.

Submitted for publication:

(With Louise Malloch) Arithmetic Properties of Bernoulli-Padé Numbers and Polynomials.

(With Kurt Girstmair) Dedekind Sums and Equal Distributions.

Fermat Numbers and Wieferich Primes: Computations and Generalizations.

Last updated: February 1, 2001. Back to homepage