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On the action of the \(U_p\) operator on the local (at p) representation attached to congruence level Siegel modular forms

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Abstract

In this article, we study the action of the \(U_p\) Hecke operator on the normalized spherical vector \(\phi \) in the representation of \({{\mathrm{GSp}}}_4(\mathbf {Q}_p)\) induced from a character on the Borel subgroup. We compute the Petersson norm of \(U_p \phi \) in terms of certain local L-values associated with \(\phi \).

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Correspondence to Jim Brown.

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The first author was partially supported by the National Security Agency under Grant Number H98230-11-1-0137. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein. The work of the second author was supported by a grant from the Simons Foundation (#354890, Krzysztof Klosin). In addition, the second author was partially supported by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York.

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Brown, J., Klosin, K. On the action of the \(U_p\) operator on the local (at p) representation attached to congruence level Siegel modular forms. Ramanujan J 44, 597–615 (2017). https://doi.org/10.1007/s11139-016-9833-x

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  • DOI: https://doi.org/10.1007/s11139-016-9833-x

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