Abstract
Let (λf (n))n⩾1 be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f. We prove that, for any fixed η > 0, under the Ramanujan-Petersson conjecture for GL2 Maass forms, the Rankin-Selberg coefficients (λf (n)2)n⩾1 admit a level of distribution θ = 2/5 + 1/260 − η in arithmetic progressions.
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Acknowledgements
The third author was supported by the SNF (Grant No. 200021_197045). We would like to thank Bingrong Huang for sharing his work [8] which gave us the motivation for writing up this note. We thank the referees for their helpful suggestions. Chen’s 2N = p + P2 Theorem is one of the greatest classics of the Analytic Number Theory literature and, as students, it gave us the impetus to pursue in this area. It is therefore a great pleasure to dedicate this work to the memory of Jingrun Chen on the occasion of the 50th anniversary of his landmark theorem.
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In memory of Jingrun Chen
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Kowalski, E., Lin, Y. & Michel, P. Rankin-Selberg coefficients in large arithmetic progressions. Sci. China Math. 66, 2767–2778 (2023). https://doi.org/10.1007/s11425-023-2155-6
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DOI: https://doi.org/10.1007/s11425-023-2155-6