Year: 2025
Type: article
Abstract: Let $q$, $m$, $n$ be any integer with $q\ge 3$, and $\lambda$ a Dirichlet character $\bmod $ $q$. An explicit formula for the fourth power mean $$ \mathop{\sum}_{{m=1}\atop{(m,q)=1}}^{q} \biggl| \mathop{\sum}_{a=1}^{q} \lambda(a) e\biggl( \frac{ma^3+na}{q} \biggr) \biggr|^4 $$ is derived. Previously, only the prime modulus $q=p$ case was studied. Let $q$, $m$, $n$ be any integer with $q\ge 3$, and $\lambda$ a Dirichlet character $\bmod $ $q$. An explicit formula for the fourth power mean $$ \mathop{\sum}_{{m=1}\atop{(m,q)=1}}^{q} \biggl| \mathop{\sum}_{a=1}^{q} \lambda(a) e\biggl( \frac{ma^3+na}{q} \biggr) \biggr|^4 $$ is derived. Previously, only the prime modulus $q=p$ case was studied.
Source: Mathematical Reports
Authors: Yaya Mu, Tianping Zhang
Institutions: Shaanxi Normal University, Northwest University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G3628969712, 指数和、特征和的相消性及相关问题研究
OpenAlex ID: W4410892280