On two conjectural series involving Riemann zeta function

2023/10/07 by Chuanan Wei, Wei, Chuanan, Ce Xu +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2310.04642

openalex publication_date 2023/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Riemann zeta function. Two of them are series expansions for ζ(7) and ζ(3)² recently conjectured by Z.-W. Sun.

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