The first moment of quadratic Dirichlet L-functions

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.

24 pages. v2: Fixed typos in the statements of Theorem 1.1 and Remark 2.2. v3: Improved notation and fixed typos

References in corpus (1)

• Mean values with cubic characters

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• The Shintani double zeta functions
• Extreme central values of quadratic Dirichlet $L$-functions with prime conductors
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• Weighted first moments of some special quadratic Dirichlet $L$-functions
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• First Moment of Quadratic Hecke $L$-Functions with Lower Order Term
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