The first moment of quadratic twists of modular $L$-functions

We obtain an asymptotic formula with an error term $O(X^{\frac{1}{2} + \varepsilon})$ for the smoothed first moment of quadratic twists of modular $L$-functions. We also give a similar result for the smoothed first moment of the first derivative of quadratic twists of modular $L$-functions. The argu...

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Bibliographic Details
Main Author Shen, Quanli
Format Journal Article
LanguageEnglish
Published 22.03.2021
Subjects
Mathematics - Number Theory
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Summary:We obtain an asymptotic formula with an error term $O(X^{\frac{1}{2} + \varepsilon})$ for the smoothed first moment of quadratic twists of modular $L$-functions. We also give a similar result for the smoothed first moment of the first derivative of quadratic twists of modular $L$-functions. The argument is largely based on Young's works (Acta Arith 138(1):73-99, 2009 and Selecta Math 19(2):509-543, 2013).
DOI:10.48550/arxiv.2103.12284