On the Rankin–Selberg problem

@article{Huang2020OnTR,
  title={On the Rankin–Selberg problem},
  author={Bingrong Huang},
  journal={arXiv: Number Theory},
  year={2020}
}
  • Bingrong Huang
  • Published 3 February 2020
  • Mathematics
  • arXiv: Number Theory
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 $\mathrm{GL}(2)$ 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. 
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