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Mean values of some Hecke characters

Volume 187 / 2019

Peng Gao, Liangyi Zhao Acta Arithmetica 187 (2019), 125-141 MSC: 11L05, 11L40, 11R11. DOI: 10.4064/aa170827-9-3 Published online: 14 November 2018


We evaluate a smoothed character sum involving $\newcommand{\bleg}[2]{\big(\frac{#1}{#2}\big)}\sum_{m}\sum_{n}\bleg {m}{n}$, where $\newcommand{\bleg}[2]{\big(\frac{#1}{#2}\big)}\bleg{m}{n}$ is a quadratic, cubic or quartic Hecke character, and the two sums over $m$ and $n$ are of comparable lengths.


  • Peng GaoSchool of Mathematics and Systems Science
    Beihang University
    Beijing 100191, China
  • Liangyi ZhaoSchool of Mathematics and Statistics
    University of New South Wales
    Sydney, NSW 2052, Australia

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