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<p>We extend a formula of Duke, Imamōglu, and Tóth (which itself is a generalization of the Katok-Sarnak formula) to give a short proof of the Kohnen-Zagier formula for Maass forms for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1213_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma _0(4)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Γ</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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A short proof of the Kohnen-Zagier formula for Maass forms for \(\Gamma _0(4)\)

  • 期刊论文

  • 发表日期：

    2025年9月16日

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  • Nickolas Andersen

摘要

We extend a formula of Duke, Imamōglu, and Tóth (which itself is a generalization of the Katok-Sarnak formula) to give a short proof of the Kohnen-Zagier formula for Maass forms for \(\Gamma _0(4)\) Γ 0 ( 4 ) .