On $p$-adic Euler $L$-functions
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.
Cite
@article{arxiv.1010.4440,
title = {On $p$-adic Euler $L$-functions},
author = {Su Hu and Min-Soo Kim},
journal= {arXiv preprint arXiv:1010.4440},
year = {2020}
}
Comments
This paper has been withdrawn, because its main results have been included in the final version of arXiv:1010.2269