# On the Rankin–Selberg problem

@article{Huang2020OnTR, title={On the Rankin–Selberg problem}, author={Bingrong Huang}, journal={arXiv: Number Theory}, year={2020} }

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.

## 10 Citations

Analytic Twists of GL3 × GL2 Automorphic Forms

- MathematicsInternational Mathematics Research Notices
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Let $\pi $ be a Hecke–Maass cusp form for $\textrm{SL}_3(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _{\pi }(n,r)$. Let $f$ be a holomorphic or Maass cusp form for…

Averages of coefficients of a class of degree 3 L-functions

- MathematicsThe Ramanujan Journal
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In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three L -functions which can be factorized as a product of a degree one and a degree two L…

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The subconvexity problem of automorphic L-functions on the critical line is one of the central problems in number theory. Subconvexity bounds have many very important applications such as the…

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The subconvexity problem of automorphic L-functions on the critical line is one of the central problems in number theory. In general, let C denote the analytic conductor of the relevant L-function,…

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The subconvexity problem of automorphic L-functions on the critical line is one of the central problems in number theory, which have very important applications to equidistribution problems. The…

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- 2021

Abstract. In this paper, we prove uniform bounds for GL(3) × GL(2) L-functions in the GL(2) spectral aspect and the t aspect by a delta method. More precisely, let φ be a Hecke–Maass cusp form for…

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We prove uniform versions of two classical results in analytic number theory.
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Uniform subconvex bounds for Rankin-Selberg $L$-functions

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- 2021

Let f be a Maass cusp form for SL2(Z) with Laplace eigenvalue 1/4 + μ 2 f , μf > 0. Let g be an arbitrary but fixed holomorphic or Maass cusp form for SL2(Z). In this paper, we establish the…

hybrid subconvexity bounds for twists of $\rm GL(3)$ $L$-functions

- Mathematics
- 2021

Let π be a SL(3,Z) Hecke-Maass cusp form and χ a primitive Dirichlet character of prime power conductor q = p with p prime. In this paper we will prove the following subconvexity bound

Analytic twists of $\rm GL_2\times\rm GL_2$ automorphic forms

- Mathematics
- 2019

Let f and g be holomorphic or Maass cusp forms for SL2(Z) with normalized Fourier coefficients λf (n) and λg(n), respectively. In this paper, we prove nontrivial estimates for the sum ∞

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Let $\pi $ be a Hecke–Maass cusp form for $\textrm{SL}_3(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _{\pi }(n,r)$. Let $f$ be a holomorphic or Maass cusp form for…

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Let f and g be holomorphic or Maass cusp forms for SL2(Z) with normalized Fourier coefficients λf (n) and λg(n), respectively. In this paper, we prove nontrivial estimates for the sum ∞

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