On the Rankin-Selberg method for vector valued Siegel modular forms

Bouganis, A.; Mercuri, S.

Abstract

In this work we use the Rankin-Selberg method to obtain results on the analytic properties of the standard L-function attached to vector valued Siegel modular forms. In particular we provide a detailed description of its possible poles and obtain a non-vanishing result of the twisted L-function beyond the usual range of absolute convergence. Our results include also the case of metaplectic Siegel modular forms. We remark that these results were known in this generality only in the case of scalar weight Siegel modular forms. As an interesting by-product of our work we establish the cuspidality of some theta series.

Citation

Bouganis, A., & Mercuri, S. (2021). On the Rankin-Selberg method for vector valued Siegel modular forms. International Journal of Number Theory, 17(5), 1207-1242. https://doi.org/10.1142/s1793042121500330

• Journal Article Type: Article
• Acceptance Date: Sep 18, 2020
• Online Publication Date: Nov 21, 2020
• Publication Date: 2021-06
• Deposit Date: Nov 7, 2018
• Publicly Available Date: Nov 21, 2021
• Journal: International Journal of Number Theory
• Print ISSN: 1793-0421
• Electronic ISSN: 1793-7310
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 5
• Pages: 1207-1242
• DOI: https://doi.org/10.1142/s1793042121500330
• Public URL: https://durham-repository.worktribe.com/output/1314001