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<p>Let <i>f</i> be a normalized Maass cusp form for the full modular group <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1242_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(\operatorname {SL}_{2} (\mathbb {Z} )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>SL</mo> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, and denote its <i>n</i>th Fourier coefficient by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1242_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda _{f}(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>λ</mi> <mi>f</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we mainly give the bound of the hybrid problem of ternary quadratic forms and the normalized Fourier coefficients of Maass cusp forms.</p>

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Quadratic forms attached to Fourier coefficients of Maass cusp forms at square-free points

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Liqun Hu,
  • Siqi Liu

摘要

Let f be a normalized Maass cusp form for the full modular group \(\operatorname {SL}_{2} (\mathbb {Z} )\) SL 2 ( Z ) , and denote its nth Fourier coefficient by \(\lambda _{f}(n)\) λ f ( n ) . In this paper, we mainly give the bound of the hybrid problem of ternary quadratic forms and the normalized Fourier coefficients of Maass cusp forms.