Fourier-Eisenstein transform and plancherel formula for rational binary quadratic forms

Yumiko Hironaka, Fumihiro Sato
1992 Nagoya mathematical journal  
LetXbe the space of nondegenerate rational symmetric matrices of size 2 and putThe groupGacts onXbyWe are interested in the space(Γ\X) of Γ-invariant C-valued functions onXand its subspace&(Γ\X)of functions whose supports consist of a finite number of Γ-orbits. The Hecke algebra ℋ(G,Γ)ofGwith respect to Γ acts naturally on these spaces.
doi:10.1017/s0027763000004244 fatcat:uwa5h2ohlnhf5ias4bu5tgtexi