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On zeta functions of orthogonal groups of single-class positive definite quadratic forms

Author(s): A. Andrianov
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 4.
Journal: St. Petersburg Math. J. 17 (2006), 553-579.
MSC (2000): Primary 11F27, 11F46, 11F60, 14G10, 20C08
Posted: May 3, 2006
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Abstract: Representations of Hecke-Shimura rings of integral single-class positive definite quadratic forms on relevant spaces of harmonic forms are considered, and the problem of simultaneous diagonalization of the corresponding Hecke operators is investigated. Explicit relations are deduced between zeta functions of the single-class quadratic forms in two and four variables corresponding to the harmonic eigenforms of genus $ 1$ and $ 2$, respectively, and zeta functions of the theta-series weighted by these eigenforms.

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Additional Information:

A. Andrianov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: anandr@pdmi.ras.ru

DOI: 10.1090/S1061-0022-06-00920-4
PII: S 1061-0022(06)00920-4
Keywords: Harmonic forms, Hecke--Shimura rings, Hecke operators, modular forms in one and several variables, theta-series of integral quadratic forms, zeta functions of quadratic forms, zeta functions of modular forms
Received by editor(s): 1/APR/2005
Posted: May 3, 2006
Additional Notes: Supported in part by the RFBR (grant no. 05-01-00930)
Copyright of article: Copyright 2006, American Mathematical Society

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