Let f be an <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1054_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">$SL(2,\mathbb {Z})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> Hecke–Maass form with normalized Fourier coefficients <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1054_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda _f(m)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>λ</mi> <mi>f</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We give a quantitative result on the number of sign changes of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1054_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda _f(m)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>λ</mi> <mi>f</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for the indices m that are the sum of two squares in the interval [1, x] for sufficiently large x.

Sign changes of Fourier coefficients of $SL(2,\mathbb {Z})$ Hecke–Maass forms at sum of two squares

期刊论文
发表日期：

2025年4月3日

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Amrinder Kaur,
Biswajyoti Saha

摘要

Let f be an $SL(2,\mathbb {Z})$ $S L (2, Z)$ Hecke–Maass form with normalized Fourier coefficients $\lambda _f(m)$ $λ_{f} (m)$ . We give a quantitative result on the number of sign changes of $\lambda _f(m)$ $λ_{f} (m)$ for the indices m that are the sum of two squares in the interval [1, x] for sufficiently large x.

Sign changes of Fourier coefficients of \(SL(2,\mathbb {Z})\) Hecke–Maass forms at sum of two squares

摘要