An analogue of Selberg's formula for Motohashi's product

TL;DR

This paper establishes an analogue of Selberg's explicit formula for Motohashi's product and derives a zero-density theorem based on Soundararajan's results, advancing understanding of the distribution of zeros in number theory.

Contribution

It introduces a new explicit formula for Motohashi's product and proves a zero-density theorem using recent results on zeta-function moments.

Findings

Derived an explicit formula for Motohashi's product

Established a zero-density theorem for the product

Connected zero distribution to zeta-function moments

Abstract

We prove an analogue of Selberg's explicit formula for Motohashi's product (see arXiv:1104.1358v3 [math.NT]). We also provide a zero-density theorem for the product, which follows from Soundararajan's theorem for moments of the Riemann zeta-function on the critical line.