On triple correlation sums of Fourier coefficients of cusp forms
Let $ p $ be a prime. In this paper, we study the sum $ \sum\limits_{m\ge 1} \sum\limits_{n\ge 1} a_n \lambda_g(m)\lambda_{f}(m+pn) \,U{ \left( \frac{m}{X} \right) }V{ \left ( \frac{n}{H} \right)} $ for any newforms $ g\in \mathcal{B}_k(1) $ (or $ \mathcal{B}_\lambda^\ast(1) $) and $ f\in...
| Autors principals: | , |
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| Format: | Article |
| Idioma: | English |
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AIMS Press
2022-09-01
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| Col·lecció: | AIMS Mathematics |
| Matèries: | |
| Accés en línia: | https://www.aimspress.com/article/doi/10.3934/math.20221063?viewType=HTML |
| Sumari: | Let $ p $ be a prime. In this paper, we study the sum
$ \sum\limits_{m\ge 1} \sum\limits_{n\ge 1} a_n \lambda_g(m)\lambda_{f}(m+pn) \,U{ \left( \frac{m}{X} \right) }V{ \left ( \frac{n}{H} \right)} $
for any newforms $ g\in \mathcal{B}_k(1) $ (or $ \mathcal{B}_\lambda^\ast(1) $) and $ f\in \mathcal{B}_k(p) $ (or $ \mathcal{B}_\lambda^\ast(p) $), with the aim of determining the explicit dependence on the level, where $ {\bf{a}} = \{a_n\in\mathbb{C}\} $ is an arbitrary complex sequence. As a result, we prove a uniform bound with respect to the level parameter $ p $, and present that this type of sum is non-trivial for any given $ H, X\ge 2 $. |
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| ISSN: | 2473-6988 |