PreprintCC BY 4.0arXiv
On the special values of Berndt's generalized L-function
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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BibTeX
@misc{he2026special,
title = {{On the special values of Berndt's generalized $L$-function}},
author = {Yuan He},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29636},
eprint = {2608.29636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29636},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the special values of Berndt's generalized L-function
AU - Yuan He
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29636
UR - https://arxiv.org/abs/2608.29636
AB - 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.
ER -