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<p>In this paper, we use properties of the <i>n</i>-order character modulo <i>p</i> and estimates for character sums over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> to study fourth power mean values of generalized Gauss sums weighted by Dirichlet <i>L</i>-functions. Our results extended the results obtained by Zhang (2002) and Bag (2024) and corrected the principal coefficient for the 4-th power moment in Bag’s paper (2024).</p>

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Moments of the generalized Gauss sum weighted by Dirichlet L-functions

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Sen Xu,
  • Tianping Zhang

摘要

In this paper, we use properties of the n-order character modulo p and estimates for character sums over \(\mathbb {F}_p\) F p to study fourth power mean values of generalized Gauss sums weighted by Dirichlet L-functions. Our results extended the results obtained by Zhang (2002) and Bag (2024) and corrected the principal coefficient for the 4-th power moment in Bag’s paper (2024).