Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions

Liangyi Zhao; Peng Gao

Twisted first moment of central values of primitive quadratic Dirichlet $L$-functions

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arxiv 2405.15980 v2 pith:ZPYIPHBG submitted 2024-05-24 math.NT

Peng Gao , Liangyi Zhao This is my paper · ORCID

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keywords dirichletcentralfirstfunctionsmainmomentprimitivequadratic

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abstract

We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet $L$-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error term of size that is the square root of that of the main term.

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First moment of quadratic Dirichlet $L$-functions with secondary terms
math.NT 2025-09 conditional novelty 7.0 of 10

Conditionally on the Riemann hypothesis and the generalized Lindelöf hypothesis, the first moment of quadratic Dirichlet L-functions has error O(X^{1/4+ε}) and lower-order terms X^{1/3} log X.

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