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arXiv · 1505.07049

Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms

Dermot McCarthy
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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 $a(I) \neq 0$. 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 $a(0)\neq 0$. From this latter case, we give simple expressions for the eigenvalues associated to degree 2 Siegel Eisenstein series.

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Dermot McCarthy. 2015-05-26. Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms. https://arxiv.org/abs/1505.07049

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