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<p>The Kloosterman sums appear as supercharacter values of a supercharacter theory induced by the group action of a subgroup of GL<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_2(\mathbb {F}_p)\)</EquationSource> </InlineEquation> on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {F}_p^2\)</EquationSource> </InlineEquation>. Using this, we here express the fifth degree mixed moment of Kloosterman sums in terms of trace of Frobenius endomorphism of certain families of elliptic curves.</p>

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Fifth Degree Mixed Moment of Kloosterman Sums, Supercharacter Theory, and Elliptic Curves

  • 期刊论文

  • 发表日期：

    2025年11月12日

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  • Fahim Sayed,
  • Gautam Kalita

摘要

The Kloosterman sums appear as supercharacter values of a supercharacter theory induced by the group action of a subgroup of GL \(_2(\mathbb {F}_p)\) on \(\mathbb {F}_p^2\) . Using this, we here express the fifth degree mixed moment of Kloosterman sums in terms of trace of Frobenius endomorphism of certain families of elliptic curves.