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    • The second moment of the Fourier coefficients of triple product $L$-functions

      HUAFENG LIU

      Article Volume 133 Published: 6 April 2023 Article ID 0008

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/133/0008

    • Keywords

       

      Fourier coefficients; triple product $L$-function; variance.

    • Abstract

       

      Suppose that $\mathbb{H}^∗$ is the set of all primitive cusp forms $f$ of even integral weight $k \geq 2$ for the full modular group $SL_2(\mathbb{Z})$. In this paper, we establish asymptotic formulas for the second moment of Fourier coefficients of the triple product $L$-function $L(s, f \otimes f \otimes f )$ and the related $L$-function $L(s, {\rm sym}^2 f \otimes f)$ attached to $f$ on average, which improves previous results.

    • Author Affiliations

       

      HUAFENG LIU1

      1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, Shandong, China

    • Dates

       
      Published
      6 April 2023
      Manuscript received
      6 June 2022
      Manuscript revised
      14 January 2023
      Accepted
      16 February 2023
      Final version published online
      6 April 2023

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