On $p$-adic Euler $L$-functions

Details On $p$-adic Euler $L$-functions On $p$-adic Euler $L$-functions

2010-10-21

arxiv.org/abs/1010.4440v2

Mathematics

Number Theory

17 pages, Corrected typos

Scientific paper

In this paper, we define the p-adic Euler L-functions using the fermionic p-adic integral on Zp. By computing the values of the p-adic Euler L-functions at negative integers, we show that for Dirichlet characters with odd conductor, this definition is quivalent to the previous definition following Kubata-Leopoldt and Washington's approach. We also study the behavior of p-adic Euler L-functions at positive integers. An interesting thing is that most of the results in Section 11.3.3 of Cohen's book [H. Cohen, Number Theory Vol. II: Analytic and Modern Tools, Graduate Texts in Mathematics, 240. Springer, New York, 2007] are also established if we replace the generalized Bernoulli numbers with the generalized Euler numbers.

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