On interaction of Hecke-Shimura rings: symplectic versus orthogonal

Anatoli Andrianov

Displaying similar documents to “On interaction of Hecke-Shimura rings: symplectic versus orthogonal”

Interaction sums and action of Hecke operators on theta-series

Anatoli Andrianov (2009)

Acta Arithmetica

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Theta Series on the Hecke Groups G(...2) and G(...3).

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Action of Hecke Operator T(p) on Theta Series.

Anatolii N. Andrianov (1980)

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The universality theorem for Hecke L-functions

Hidehiko Mishou (2003)

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Theta liftings and Hecke L-functions.

Tonghai Yang (1997)

Journal für die reine und angewandte Mathematik

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Action of Hecke operators on products of Igusa theta constants with rational characteristics

Anatoli N. Andrianov, Fedor A. Andrianov (2004)

Acta Arithmetica

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On quadratic character twists of Hecke L-functions attached to cusp forms of varying weights at the central point

W. Kohnen, J. Sengupta (2001)

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Hecke operators for GLₙ and buildings

Cristina M. Ballantine, John A. Rhodes, Thomas R. Shemanske (2004)

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Products of an arbitrary number of Hecke eigenforms

Brad A. Emmons, Dominic Lanphier (2007)

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On Automorphic Forms on the Unitary Symplectic Group Sp (n) and SL2 (R).

Tomoyoshi Ibukiyama, Yasutaka Ihara (1987)

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Explicit Hecke series for symplectic group of genus 4

Kirill Vankov (2011)

Journal de Théorie des Nombres de Bordeaux

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Shimura conjectured the rationality of the generating series for Hecke operators for the symplectic group of genus $n$ . This conjecture was proved by Andrianov for arbitrary genus $n$ , but the explicit expression was out of reach for genus higher than 3. For genus $n = 4$ , we explicitly compute the rational fraction in this conjecture. Using formulas for images of double cosets under the Satake spherical map, we first compute the sum of the generating series, which is a rational fraction with...