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Rankin-Selberg coefficients in large arithmetic progressions

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Emmanuel Kowalski, Yongxiao Lin, Philippe Michel

Number Theory · Submitted 17 Apr 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that, for any fixed $\eta>0$, under the Ramanujan-Petersson conjecture for $\rm GL_2$ Maass forms, the Rankin-Selberg coefficients $(\lambda_f(n)^2)_{n\geq 1}$ admit a level of distribution $\theta=2/5+1/260-\eta$ in arithmetic progressions.

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arXiv ID2304.08231 (version 2)
Pith IDJ2QIFU7H, Pith's permanent record of this paper and its review
CitationEmmanuel Kowalski, Philippe Michel, Yongxiao Lin. "Rankin-Selberg coefficients in large arithmetic progressions." arXiv:2304.08231 (2023). https://pith.science/paper/J2QIFU7H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,479 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.83 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.06 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; .

Let $(\lambda_f(n))_{n\geq 1}$ be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form $f$. We prove that, for any fixed $\eta>0$, under the Ramanujan-Petersson conjecture for $\rm GL_2$ Maass forms, the Rankin-Selberg coefficients $(\lambda_f(n)^2)_{n\geq 1}$ admit a level of distribution $\theta=2/5+1/260-\eta$ in arithmetic progressions.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let $(\lambda_f(n))_{n\geq 1}$ be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form $f$. background 1.00 0.08 0.02 asserted 0.86
s1 We prove that, for any fixed $\eta>0$, under the Ramanujan-Petersson conjecture for $\rm GL_2$ Maass forms, the Rankin-Selberg coefficients $(\lambda_f(n)^2)_{n\geq 1}$ admit a level of distribution $\theta=2/5+1/260-\eta$ in arithmetic progressions. result 0.95 0.94 0.95 asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

Let $(\lambda_f(n))_{n\geq 1}$ be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form $f$. We prove that, for any fixed $\eta>0$, under the Ramanujan-Petersson conjecture for $\rm GL_2$ Maass forms, the Rankin-Selberg coefficients $(\lambda_f(n)^2)_{n\geq 1}$ admit a level of distribution $\theta=2/5+1/260-\eta$ in arithmetic progressions.

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