Inverting the Satake map for \(\text{Sp}_n\) and applications to Hecke operators

DOI10.1007/s11139-007-9035-7zbMath1213.11108OpenAlexW2054309422MaRDI QIDQ1024102

Thomas R. Shemanske, Nathan C. Ryan

Publication date: 16 June 2009

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-007-9035-7

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Hecke-Petersson operators, differential operators (several variables) (11F60)

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Cites Work

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• Das Vertauschungsgesetz zwischen Hecke-Operatoren und dem Siegelschen \(\Phi\) -Operator. (The commutation property between Hecke operators and Siegel's \(\Phi\) -operator)
• Rationality theorems for Hecke operators on GL\(_n\).
• Theory of spherical functions on reductive algebraic groups over p-adic fields
• On a conjecture of Duke-Imamoglu
• Siegel modular forms, \(L\)-functions, and Satake parameters