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Testing the
functional equation of a high-degree Euler product
David W. Farmer, Nathan C. Ryan and Ralf Schmidt |
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Vol. 253 (2011), No. 2, 349–366
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Abstract |
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We study the L-functions associated to Siegel modular forms—equivalently, automorphic representations of GSp(4, 𝔸ℚ)—both theoretically and numerically. For the L-functions of degrees 10, 14, and 16 we perform representation theoretic calculations to cast the Langlands L-function in classical terms. We develop a precise notion of what it means to test a conjectured functional equation for an L-function, and we apply this to the degree-10 adjoint L-function associated to a Siegel modular form. |
Keywords
Siegel modular forms, L-functions
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Mathematical Subject Classification 2000
Primary: 11F46, 11F66
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Milestones
Received: 13 October 2008
Revised: 10 September 2010
Accepted: 31 January 2011
Published: 21 January 2012
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Authors |
| David W. Farmer | |
| American Institute of
Mathematics Palo Alto, CA 94306 United States |
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| Nathan C. Ryan | |
| Department of Mathematics Bucknell University Lewisburg, PA 17837 United States |
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| Ralf Schmidt | |
| Department of Mathematics University of Oklahoma Norman, OK 73072 United States |
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