On the Rankin-Selberg problem

DOI10.1007/S00208-021-02186-7zbMATH Open1483.11098arXiv2002.00591OpenAlexW3003951394MaRDI QIDQ832475

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Publication date: 25 March 2022

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Abstract: In this paper, we solve the Rankin--Selberg problem. That is, we break the well known Rankin--Selberg's bound on the error term of the second moment of Fourier coefficients of a $mathrmGL(2)$ cusp form (both holomorphic and Maass), which remains its record since its birth for more than 80 years. We extend our method to deal with averages of coefficients of L-functions which can be factorized as a product of a degree one and a degree three L-functions.

Full work available at URL: https://arxiv.org/abs/2002.00591

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