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December 2008 Bernoulli numbers and zeros of $p$-adic $L$-functions
Tauno Metsänkylä
Funct. Approx. Comment. Math. 39(2): 223-235 (December 2008). DOI: 10.7169/facm/1229696573

Abstract

Rational $p$-adic zeros of the Leopoldt-Kubota $p$-adic $L$-functions give rise to certain sequences of generalized Bernoulli numbers tending $p$-adically to zero, and conversely. This relationship takes different forms depending on whether the corresponding Iwasawa $\lambda$-invariant is one or greater than one. To understand the relationship better it is useful to consider approximate zeros of those functions.

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Tauno Metsänkylä. "Bernoulli numbers and zeros of $p$-adic $L$-functions." Funct. Approx. Comment. Math. 39 (2) 223 - 235, December 2008. https://doi.org/10.7169/facm/1229696573

Information

Published: December 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1203.11078
MathSciNet: MR2490738
Digital Object Identifier: 10.7169/facm/1229696573

Subjects:
Primary: 11B68
Secondary: 11R23 , 11S40

Keywords: $p$-adic $L$-functions and their zeros , Bernoulli numbers , generalized Bernoulli numbers , Iwasawa $\lambda$-invariants

Rights: Copyright © 2008 Adam Mickiewicz University

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Vol.39 • No. 2 • December 2008
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