Contour Integrations and Parity Results of Hurwitz-type Cyclotomic Euler Sums
Number Theory
2026-01-05 v1
Abstract
In this paper, we investigate the parity of three class of Hurwitz-type cyclotomic Euler sums using the methods of contour integration and residue computation, and derive explicit parity formulas for linear, quadratic, and some higher-order cases. Based on their connection with cyclotomic multiple Hurwitz polylogarithm functions, we further obtain certain parity results for these functions. At the end of the paper, we propose two conjectures regarding the parity and symmetry of multiple Hurwitz polylogarithm functions of arbitrary depth.
Keywords
Cite
@article{arxiv.2601.00035,
title = {Contour Integrations and Parity Results of Hurwitz-type Cyclotomic Euler Sums},
author = {Hongyuan Rui},
journal= {arXiv preprint arXiv:2601.00035},
year = {2026}
}
Comments
31 pages. arXiv admin note: text overlap with arXiv:2509.17468 by other authors