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- Title
On some estimates involving Fourier coefficients of Maass cusp forms.
- Authors
Sun, Qingfeng; Wang, Hui
- Abstract
Let f be a Hecke–Maass cusp form for SL 2 (ℤ) with Laplace eigenvalue λ f (Δ) = 1 / 4 + μ 2 and let λ f (n) be its n th normalized Fourier coefficient. It is proved that, uniformly in α , β ∈ ℝ , ∑ n ≤ X λ f (n) e (α n 2 + β n) ≪ X 7 / 8 + λ f (Δ) 1 / 2 + , where the implied constant depends only on . We also consider the summation function of λ f (n) and under the Ramanujan conjecture we are able to prove ∑ n ≤ X λ f (n) ≪ X 1 / 3 + λ f (Δ) 4 / 9 + with the implied constant depending only on .
- Subjects
CUSP forms (Mathematics); EXPONENTIAL sums; EIGENVALUES; LOGICAL prediction
- Publication
International Journal of Number Theory, 2023, Vol 19, Issue 5, p997
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042123500495