Various conjectural series identities
Number Theory
2026-04-14 v3 Combinatorics
Abstract
In this paper we collect over 150 new series identities (involving binomial coefficients) conjectured by the author in 2026. The values involved are related to or Riemann's zeta function or Dirichlet's -function. For example, we conjecture that where denotes the coefficient of in the expansion of . The conjectures in this paper might interest some readers and stimulate further research.
Cite
@article{arxiv.2603.29973,
title = {Various conjectural series identities},
author = {Zhi-Wei Sun},
journal= {arXiv preprint arXiv:2603.29973},
year = {2026}
}
Comments
27 pages. Mainly add Section 5