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

Andrianov, A.

doi:10.1090/S1061-0022-06-00920-4

On zeta functions of orthogonal groups of single-class positive definite quadratic forms
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by A. Andrianov
Translated by: the author

St. Petersburg Math. J. 17 (2006), 553-579

DOI: https://doi.org/10.1090/S1061-0022-06-00920-4

Published electronically: 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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