pith. sign in

arxiv: 2303.15856 · v2 · pith:5NOEIIVFnew · submitted 2023-03-28 · 🧮 math.NT

Sum of the GL(3) Fourier coefficients over quadratics

classification 🧮 math.NT
keywords leqslantequationfourierarticleasymptoticbegincoefficientcoefficients
0
0 comments X
read the original 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 $Y\leqslant X$.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.