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

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    • 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



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

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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