On two conjectural series involving the Riemann zeta function

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发表日期：

2025年7月30日

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Chuanan Wei,
Ce Xu

摘要

The Riemann zeta function is important in a lot of branches of number theory. With the help of the operator method and several transformation formulas for hypergeometric series, we prove four series involving the Riemann zeta function. Two of them are series expansions for $\zeta (7)$ $ζ (7)$ and $\zeta (3)^2$ $ζ {(3)}^{2}$ recently conjectured by Z.-W. Sun.