First moment of central values of quadratic Dirichlet $L$-functions

Published 21 Mar 2023 in math.NT | (2303.11588v4)

Abstract: We evaluate the first moment of central values of the family of quadratic Dirichlet $L$-functions using the method of double Dirichlet series. Under the generalized Riemann hypothesis, we prove an asymptotic formula with an error term of size that is the fourth root of that of the primary main term.

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