Bounds of divided universal Bernoulli numbers and universal Kummer congruences
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- by Arnold Adelberg, Shaofang Hong and Wenli Ren PDF
- Proc. Amer. Math. Soc. 136 (2008), 61-71 Request permission
Abstract:
Let $p$ be a prime. We obtain good bounds for the $p$-adic sizes of the coefficients of the divided universal Bernoulli number $\tfrac {\hat {B}_n}{n}$ when $n$ is divisible by $p-1$. As an application, we give a simple proof of Clarke’s 1989 universal von Staudt theorem. We also establish the universal Kummer congruences modulo $p$ for the divided universal Bernoulli numbers for the case $(p-1)|n$, which is a new result.References
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Additional Information
- Arnold Adelberg
- Affiliation: Department of Mathematics, Grinnell College, Grinnell, Iowa 50112-0806
- Email: adelbe@math.grinnell.edu
- Shaofang Hong
- Affiliation: Mathematical College, Sichuan University, Chengdu 610064, People’s Republic of China
- Email: s-f.hong@tom.com, hongsf02@yahoo.com
- Wenli Ren
- Affiliation: Mathematical College, Sichuan University, Chengdu 610064, People’s Republic of China, and Department of Mathematics, Dezhou University, Dezhou 253023, People’s Republic of China
- Email: renwenli80@163.com
- Received by editor(s): July 5, 2006
- Received by editor(s) in revised form: December 1, 2006
- Published electronically: August 14, 2007
- Additional Notes: The second author is the corresponding author and was supported by New Century Excellent Talents in University Grant # NCET-06-0785, and by SRF for ROCS, SEM
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 61-71
- MSC (2000): Primary 11B68, 11B83; Secondary 11A07
- DOI: https://doi.org/10.1090/S0002-9939-07-09025-9
- MathSciNet review: 2350389