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• W3201214114 startingPage "1" @default.
• W3201214114 abstract "Let $F$ be a Siegel cusp form of degree 2, even weight $k geq 2$ and odd squarefree level $N$. We undertake a detailed study of the analytic properties of Fourier coefficients $a(F,S)$ of $F$ at fundamental matrices $S$ (i.e., with $-4 det(S)$ equal to a fundamental discriminant). We prove that as $S$ varies along the equivalence classes of fundamental matrices with $det(S) asymp X$, the sequence $a(F,S)$ has at least $X^{1-epsilon}$ sign changes, and takes at least $X^{1-epsilon}$ large values. Furthermore, assuming the Generalized Riemann Hypothesis as well as the refined Gan--Gross--Prasad conjecture, we prove the bound $|a(F,S)| ll_{F, epsilon} frac{det(S)^{frac{k}2 - frac{1}{2}}}{ (log |det(S)|)^{frac18 - epsilon}}$ for fundamental matrices $S$." @default.
• W3201214114 created "2021-09-27" @default.
• W3201214114 creator A5028120984 @default.
• W3201214114 creator A5029914897 @default.
• W3201214114 creator A5084548112 @default.
• W3201214114 date "2021-11-12" @default.
• W3201214114 modified "2023-09-30" @default.
• W3201214114 title "ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 2" @default.
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• W3201214114 doi "https://doi.org/10.1017/s1474748021000542" @default.
• W3201214114 hasPublicationYear "2021" @default.
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