On two conjectures of Sun concerning Ap\'ery-like series
Number Theory
2023-09-14 v1
Abstract
In this paper, we shall prove two conjectures of Z.-W. Sun concerning Ap\'ery-like series. One of the series is alternating whereas the other one is not. Our main strategy is to convert the series (resp.~the alternating series) to log-sine-cosine (resp.~log-sinh-cosh) integrals. Then we express all these integrals in terms of single-valued Bloch-Wigner-Ramakrishnan-Wojtkowiak-Zagier polylogarithms. The conjectures then follow from a few highly non-trivial functional equations of the polylogarithms of weight and .
Keywords
Cite
@article{arxiv.2210.14704,
title = {On two conjectures of Sun concerning Ap\'ery-like series},
author = {Steven Charlton and Herbert Gangl and Li Lai and Ce Xu and Jianqiang Zhao},
journal= {arXiv preprint arXiv:2210.14704},
year = {2023}
}
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19 pages