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<p>This paper investigates the high-order moment problem of Fourier coefficients on square sum sequences related to modular symmetric power <i>L</i>-functions. We mainly focus on two types of sparse sequences: positive integers represented by the sum of six squares and the sum of four squares, and have improved the asymptotic formulas <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sum \lambda _{\textrm{sym}^j f}(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>∑</mo> <msub> <mi>λ</mi> <mrow> <msup> <mtext>sym</mtext> <mi>j</mi> </msup> <mi>f</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> related to them.</p>

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The asymptotic distribution of the Fourier coefficients of symmetric power L-function over sparse sequences

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Yukun Liu,
  • Jing Huang

摘要

This paper investigates the high-order moment problem of Fourier coefficients on square sum sequences related to modular symmetric power L-functions. We mainly focus on two types of sparse sequences: positive integers represented by the sum of six squares and the sum of four squares, and have improved the asymptotic formulas \(\sum \lambda _{\textrm{sym}^j f}(n)\) ∑ λ sym j f ( n ) related to them.