The first moment of quadratic Dirichlet L-functions

TL;DR

This paper derives an asymptotic formula for the average value of quadratic Dirichlet L-functions at the central point, with a notably improved error term achieved through a recursive method.

Contribution

It introduces a recursive approach to refine the error term in the asymptotic formula for the first moment of quadratic Dirichlet L-functions.

Findings

Asymptotic formula with square-root error term

Recursive technique improves error estimates

Enhanced understanding of L-functions at the central point

Abstract

We obtain an asymptotic formula for the smoothly weighted first moment of primitive quadratic Dirichlet L-functions at the central point, with an error term that is "square-root" of the main term. Our approach uses a recursive technique that feeds the result back into itself, successively improving the error term.