On the Rankin–Selberg problem

Bingrong Huang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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) 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.

Original languageEnglish
Pages (from-to)1217-1251
Number of pages35
JournalMathematische Annalen
Issue number3-4
StatePublished - Dec 2021
Externally publishedYes


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