Generalized Apostol-Bernoulli Functions and the Evaluation of Character Sums

Authors

• Brad Isaacson, CUNY New York City College of TechnologyFollow

Document Type

Article

Publication Date

9-28-2026

Abstract

We introduce two types of generalized Apostol–Bernoulli functions attached to Dirichlet characters and express them by generalized Apostol–Bernoulli numbers. As a corollary, we obtain formulas expressing two families of character sums by generalized Apostol–Bernoulli numbers. These sums are twisted generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko, Kim, Ramanujan, and Zaharescu in the context of modular forms and theta function identities.

Comments

This article was originally published in Integers, available at https://doi.org/10.5281/zenodo.23018126.

This work is distributed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).