1. Level aspect exponential sums involving Fourier coefficients of symmetric-square lifts.
- Author
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Hou, F.
- Subjects
- *
EXPONENTIAL sums , *AUTOMORPHIC forms , *INTEGERS - Abstract
Fix an integer κ ≥ 2 . Let P ≥ 2 be a prime, and F be the symmetric-square lift of a Hecke newform f ∈ S κ * (P) . We study the exponential sum L F (α) = ∑ n ∼ N A F (n , 1) e (n α) by implementing an average over a family in such a way to investigate the best possible magnitude of the level aspect bound for L F (α) . We prove a uniform bound with respect to any α ∈ R and the level parameter P , and present that there exist certain forms with fairly strong oscillations in L F (α) , if the associated level of f is allowed to vary. As applications, we consider the shifted convolution sums for GL (3) × GL (d) , for any d ≥ 2 , in a family as well as theWaring-Goldbach problem associated to Fourier coefficients of SL (3 , Z) -Maa β forms. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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