On analytic properties of the standard zeta function attached to a vector valued modular form
Abstract
We proof a Garrett-Böcherer decomposition of a vector valued Siegel Eisenstein series $E_{l,0}^2$ of genus 2 transforming with the Weil representation of $\text{Sp}_2(\mathbb{Z})$ on the group ring $\mathbb{C}[(L'/L)^2]$. We show that the standard zeta function associated to a vector valued common eigenform $f$ for the Weil representation can be meromorphically continued to the whole $s$-plane and that it satisfies a functional equation. The proof is based on an integral representation of this zeta function in terms of $f$ and $E_{l,0}^2$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.06540
- arXiv:
- arXiv:2108.06540
- Bibcode:
- 2021arXiv210806540S
- Keywords:
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- Mathematics - Number Theory;
- 11F27 11F25 11F66 11M41
- E-Print:
- 28 pages, submitted for publication