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On the fourth moment in the Rankin-Selberg problem

Aleksandar Ivić
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Abstract

If $$ Δ(x) := \sum_{n\le x}c_n - Cx $$ denotes the error term in the classical Rankin-Selberg problem, then it is proved that $$ \int_0^X Δ^4(x)\d x \ll_εX^{3+ε},\quad \int_0^X Δ_1^4(x)\d x \ll_εX^{11/2+ε}, $$ where $Δ_1(x) = \int_0^xΔ(u) du$. The latter bound is, up to `$ε$', best possible.

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Aleksandar Ivić. 2007-01-31. On the fourth moment in the Rankin-Selberg problem. https://arxiv.org/abs/math/0701912

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