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

A. Andrianov
2006 St. Petersburg Mathematical Journal  
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
more » ... weighted by these eigenforms.
doi:10.1090/s1061-0022-06-00920-4 fatcat:wolccxgxpnhbzkpxp7qujyaj2e