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

Bouganis, A.; Mercuri, S.

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


Authors

S. Mercuri



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.

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

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