On two conjectural series involving Riemann zeta function

TL;DR

This paper proves four series involving the Riemann zeta function using operator methods and hypergeometric transformations, including two conjectured series for ζ(7) and ζ(3)^2 by Sun.

Contribution

It introduces new proofs for conjectural series involving the Riemann zeta function using innovative operator and hypergeometric techniques.

Findings

Proof of four series involving ζ(s)

Verification of Sun's conjectured series for ζ(7) and ζ(3)^2

Application of hypergeometric transformations in number theory

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 $\zeta(7)$ and $\zeta(3)^2$ recently conjectured by Z.-W. Sun.