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

Bouganis, A. and Mercuri, S. (2021) 'On the Rankin-Selberg method for vector valued Siegel modular forms.', International journal of number theory., 17 (5). pp. 1207-1242.


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.

Item Type:Article
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Publisher statement:Electronic version of an article published as International Journal of Number Theory, 17:5, 2021, 1207-1242, © copyright World Scientific Publishing Company,
Date accepted:18 September 2020
Date deposited:22 September 2020
Date of first online publication:21 November 2020
Date first made open access:21 November 2021

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