Rankin-Selberg coefficients in large arithmetic progressions

Let (λ f ( 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 GL 2 Maass forms, the Rankin-Selberg coefficients (λ f ( n ) 2 ) n ⩾1 admit a level of distribu...

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Bibliographic Details
Published in:Science China. Mathematics 2023-12, Vol.66 (12), p.2767-2778
Main Authors: Kowalski, Emmanuel, Lin, Yongxiao, Michel, Philippe
Format: Article
Language:English
Subjects:
Applications of Mathematics
Arithmetic
Eigenvalues
Mathematical analysis
Mathematics
Mathematics and Statistics
Progressions
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Summary:Let (λ f ( 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 GL 2 Maass forms, the Rankin-Selberg coefficients (λ f ( n ) 2 ) n ⩾1 admit a level of distribution θ = 2/5 + 1/260 − η in arithmetic progressions.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-023-2155-6