On the fourth moment in the Rankin-Selberg problem

DOI10.1007/S00013-008-2326-4zbMATH Open1209.11088arXivmath/0701912OpenAlexW2077925532MaRDI QIDQ948898

Aleksandar Ivić

Publication date: 16 October 2008

Published in: Archiv der Mathematik (Search for Journal in Brave)

Abstract: If ${\displaystyle }$ Delta(x) := sum_{nle x}c_n - Cx ${\displaystyle }$ denotes the error term in the classical Rankin-Selberg problem, then it is proved that ${\displaystyle }$ int_0^X Delta^4(x)d x ll_epsilon X^{3+epsilon},quad int_0^X Delta_1^4(x)d x ll_epsilon X^{11/2+epsilon}, ${\displaystyle }$ where $Delt{a}_1(x)=in{t}_0^{x}Delta(u)du$. The latter bound is, up to `$epsilon$', best possible.

Full work available at URL: https://arxiv.org/abs/math/0701912

zbMATH Keywords

mean square estimatesRankin-Selberg problem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Fourier coefficients of automorphic forms (11F30)

Related Items (3)

On the Rankin-Selberg problem ⋮ On the Rankin-Selberg problem: higher power moments of the Riesz mean error term ⋮ On the fourth moment of Hecke–Maass forms and the random wave conjecture

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