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

Su Hu; Min-Soo Kim

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arXiv · 1010.4440

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

Su Hu·Min-Soo Kim

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Abstract

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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Su Hu, Min-Soo Kim. 2010-10-21. On $p$-adic Euler $L$-functions. https://arxiv.org/abs/1010.4440

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