Integral moment of the Riemann zeta function and Hecke $L$ functions

Zhaoyan Chen

Integral moment of the Riemann zeta function and Hecke $L$ functions

Number Theory 2025-01-15 v2

Authors: Zhaoyan Chen

Abstract

Let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$ . We prove an asymptotic formula for the mixed moment of the product of $\zeta(s)$ and $L(s,f)$ on the critical line. Similarly, we prove an asymptotic formula for the mixed moment of the product of $|\zeta^{2}(s)|$ and $L(s,f)$ on the critical line.

Keywords

Riemann zeta function Hecke L-function moment asymptotic formula critical line

Cite

@article{arxiv.2501.04348,
  title  = {Integral moment of the Riemann zeta function and Hecke $L$ functions},
  author = {Zhaoyan Chen},
  journal= {arXiv preprint arXiv:2501.04348},
  year   = {2025}
}

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