Journal of the Ramanujan Mathematical Society

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Ramanujan-Type Results for Siegel Cusp Forms of Degree 2


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1 Department of Mathematics, University of Oklahoma, Norman, OK 73019, United States
     

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A result of Chai-Faltings on Satake parameters of Siegel cusp forms together with the classification of unitary, unramified, irreducible, admissible representations of GSp4 over a p-adic field, imply that the local components of the automorphic representation of GSp4 attached to a cuspidal Siegel eigenform of degree 2 must lie in certain families. Applications include estimates on Hecke eigenvalues, an improved domain of convergence of the standard L-function, and a new characterization of the Maaß space.
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  • Ramanujan-Type Results for Siegel Cusp Forms of Degree 2

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Authors

Ameya Pitale
Department of Mathematics, University of Oklahoma, Norman, OK 73019, United States
Ralf Schmidt
Department of Mathematics, University of Oklahoma, Norman, OK 73019, United States

Abstract


A result of Chai-Faltings on Satake parameters of Siegel cusp forms together with the classification of unitary, unramified, irreducible, admissible representations of GSp4 over a p-adic field, imply that the local components of the automorphic representation of GSp4 attached to a cuspidal Siegel eigenform of degree 2 must lie in certain families. Applications include estimates on Hecke eigenvalues, an improved domain of convergence of the standard L-function, and a new characterization of the Maaß space.