1. Triple correlation sums of coefficients of cusp forms.
- Author
-
Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander
- Subjects
- *
RIEMANN hypothesis , *CUSP forms (Mathematics) , *STATISTICAL correlation , *ARITHMETIC series , *PRESIDENTIAL terms of office , *DIRICHLET series - Abstract
We produce nontrivial asymptotic estimates for shifted sums of the form ∑ a (h) b (m) c (2 m − h) , in which a (n) , b (n) , c (n) are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate how to strengthen them under the Riemann Hypothesis. As an application, we show that there are infinitely many three term arithmetic progressions n − h , n , n + h such that a (n − h) a (n) a (n + h) ≠ 0. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF