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arXiv · 2608.29636

On the special values of Berndt's generalized $L$-function

Yuan He
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Abstract

In this paper, we study the generalized $L$-function considered by Berndt (1975). We introduce the generalized Apostol-Bernoulli polynomials and the generalized Apostol-Bernoulli functions, and establish some properties for them, including the Fourier series for these functions. We show that the values of Berndt's generalized $L$-function at integers are explicitly evaluated in terms of the generalized Apostol-Bernoulli functions.

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Yuan He. 2026-08-30. On the special values of Berndt's generalized $L$-function. https://arxiv.org/abs/2608.29636

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