Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms

DOI10.1016/J.JNT.2016.06.022zbMATH Open1419.11078arXiv1505.07049OpenAlexW2963704181MaRDI QIDQ311472

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Publication date: 13 September 2016

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Abstract: We prove multiplicative relations between certain Fourier coefficients of degree 2 Siegel eigenforms. These relations are analogous to those for elliptic eigenforms. We also provide two sets of formulas for the eigenvalues of degree 2 Siegel eigenforms. The first evaluates the eigenvalues in terms of the form's Fourier coefficients, in the case $a(I)eq0$. The second expresses the eigenvalues of index $p$ and $p^2$, for $p$ prime, solely in terms of $p$ and $k$, the weight of the form, in the case $a(0)eq0$. From this latter case, we give simple expressions for the eigenvalues associated to degree 2 Siegel Eisenstein series.

Full work available at URL: https://arxiv.org/abs/1505.07049

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