Year: 2026
Type: preprint
Abstract: In this paper, we establish a summation formula associated with the generalized Apostol-Bernoulli functions. This formula unifies the Euler-Maclaurin summation formula, the Euler-Boole summation formula, and the character analogues of these two formulas. We also apply it to obtain the general power sum formula and the special values of Berndt's generalized $L$-function at non-positive integers.
Source: arXiv (Cornell University)
Author: He, Yuan
Institution: Neijiang Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206169123