On the Rankin–Selberg problem

By Bingrong Huang. Mathematische Annalen, 2020

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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 GL(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {GL}}(2)$$\end{document} 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.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

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