Size of product of a number and its multiplicative inverse, Moments of L-functions and Exponential Sums

TL;DR

This paper investigates the average size of the product of a number and its inverse modulo a prime, linking it to L-function moments and deriving an asymptotic formula for a specific exponential sum.

Contribution

It introduces a new connection between multiplicative inverses, L-function moments, and exponential sums, providing an asymptotic formula for a triple exponential sum.

Findings

Average size of product and inverse modulo p characterized

Asymptotic formula for a triple exponential sum derived

Links between inverse products and L-functions established

Abstract

In this paper, we study the average size of the product of a number and its multiplicative inverse modulo a prime p. This turns out to be related to moments of L-functions and leads to a curious asymptotic formula for a certain triple exponential sum.