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arXiv · 1608.07063

On double shifted convolution sum of $SL(2, \mathbb{Z})$ Hecke eigen forms

Saurabh Kumar Singh
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Abstract

Let $\lambda_i (n)$ $i= 1, 2, 3$ denote the normalised Fourier coefficients of holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: \[ S:= \frac{1}{H}\sum_{h\leq H} V\left( \frac{h}{H}\right)\sum_{n\leq N} \lambda_1 (n) \lambda_2 (n+h) \lambda_3 (n+ 2h)W\left( \frac{n}{N} \right), \] \noindent where $V$ and $W$ are smooth bump functions, supported on $[1, 2]$. We shall prove a nontrivial upper bound, under the assumption that $H\geq N^{1/2+ \epsilon}$.

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Saurabh Kumar Singh. 2016-08-25. On double shifted convolution sum of $SL(2, \mathbb{Z})$ Hecke eigen forms. https://arxiv.org/abs/1608.07063

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