On a convolution series attached to a Siegel Hecke cusp form of degree 2

Soumya Das; Winfried Kohnen; Jyoti Sengupta

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arXiv · 1306.4163

On a convolution series attached to a Siegel Hecke cusp form of degree 2

Soumya Das·Winfried Kohnen·Jyoti Sengupta

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Abstract

We prove that the "naive" convolution Dirichlet series D_2(s) attached to a degree 2 Siegel Hecke cusp form F, has a pole at s=1. As an application, we write down the asymptotic formula for the partial sums of the squares of the eigenvalues of $F$ with an explicit error term. Further, as a corollary, we are able to show that the abscissa of absolute convergence of the (normalized) spinor zeta function attached to F is s = 1.

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Soumya Das, Winfried Kohnen, Jyoti Sengupta. 2013-06-18. On a convolution series attached to a Siegel Hecke cusp form of degree 2. https://arxiv.org/abs/1306.4163

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