Abstract:Let $A(n)$ denote the $(1,n)\text{-th}$ Fourier coefficient of a $SL(3, \mathbb{Z})$ Hecke eigenform or the ternary divisor function $d_3(n)$. Let $Q(x,y)$ be a symmetric positive definite quadratic form. This article establishes an asymptotic formula with a power-saving error term for the following sum \begin{equation*}
\sum_{1 \leqslant m \leqslant X} \sum_{1 \leqslant n\leqslant Y} A(Q(m,n)), \end{equation*} where $X>1$ and $Y\leqslant X$.
From: Himanshi Chanana [view email]
[v1]
Tue, 28 Mar 2023 09:53:28 UTC (19 KB)
[v2]
Wed, 24 Jun 2026 09:30:05 UTC (28 KB)
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