Multiplicative arithmetic of theta-series of odd quadratic forms. (English. Russian original) Zbl 0894.11021

Zhuravlev, V. G.

Izv. Math. 59, No. 3, 517-578 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 59, No. 3, 77-140 (1995).

MSC:

11F27	Theta series; Weil representation; theta correspondences
11F46	Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F30	Fourier coefficients of automorphic forms
11E12	Quadratic forms over global rings and fields
11F66	Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F60	Hecke-Petersson operators, differential operators (several variables)

Keywords:

odd quadratic forms; symmetric Dirichlet series; lifting of automorphic eigenforms; Euler expansion; locl zeta-functions; operators of symplectic Hecke rings; theta-series of positive definite quadratic forms; generalized Eichler-Brandt matrices; linear dependence of theta-series; Siegel modular eigenforms