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

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 نشر من قبل Quanli Shen
 تاريخ النشر 2021
  مجال البحث
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 تأليف Quanli Shen




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We obtain the 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 Youngs recursive method [19,20].



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