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Exponential sums of squares of Fourier coefficients of cusp forms.
- Source :
-
Proceedings of the Indian Academy of Sciences: Mathematical Sciences . 2020, Vol. 130 Issue 1, p1-7. 7p. - Publication Year :
- 2020
-
Abstract
- We prove nontrivial estimates for linear sums of squares of Fourier coefficients of holomorphic and Maass cusp forms twisted by additive characters. For holomorphic forms f, we show that if | α - a / q | ≤ 1 / q 2 with (a , q) = 1 , then for any ε > 0 , ∑ n ⩽ X λ f (n) 2 e (n α) ≪ f , ε X 4 5 + ε for X 1 5 ≪ q ≪ X 4 5. <graphic href="12044_2019_550_Article_Equ23.gif"></graphic> Moreover, for any ε > 0 , there exists a set S ⊂ (0 , 1) with μ (S) = 1 such that for every α ∈ S , there exists X 0 = X 0 (α) such that the above inequality holds true for any α ∈ S and X ⩾ X 0 (α). A weaker bound for Maass cusp forms is also established. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02534142
- Volume :
- 130
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Proceedings of the Indian Academy of Sciences: Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 142094319
- Full Text :
- https://doi.org/10.1007/s12044-019-0550-4