INDE X adelization, 58 , 60 algebraic group , 5 8 anisotropic, 1 automorphic form , 7 8 bounded domain , 214ff . Cayley transformation , 5- 6 central simpl e algebra , 25 1 class o f lattices, 62 conductor, 23 8 congruence subgroup , 6 2 cusp form , 7 9 denominator ideal , 1 9 discriminant, 6 Eisenstein series , 94 , 96, 15 0 Fourier expansio n of , 15 1 elementary divisors , 1 7 elliptic modula r type , 7 8 £-hermitian form , 1 Euler facto r local, 133- 5 Euler product , 168 , 17 4 factor o f automorphy, 40 , 78 Fourier expansion , 20 9 of an automorphi c form , 148 , 227fT. Gauss sum , 239-4 0 genus o f lattices, 62 limited, 20 5 Hecke algebra , 8 5 Hecke character, 23 8 Hecke operator, 8 6 ideal character , 23 8 inner product , 8 1 involution, 1 main, 24 , 252 isotropic, 1 259 kernel function , 220 , 224 //-function, 23 8 lattice, 2 6 maximal, 2 6 mass, 9 9 of a genus, 20 5 of a limite d genus , 20 5 maximal order , 25 2 measure Haar, 6 5 invariant, 42 , 54, 81 modular form , 7 8 normalized Heck e character, 23 8 origin, 41 , 77 parabolic subgroup , 7 , 68 minimal, 7 primitive matrix , 1 7 quaternion algbra , 24 , 252 radical, 6 8 reduced expression , 1 9 reductive group , 6 8 regular matrix , 10 4 semisimple group , 6 8 Siegel set , 23 4 strong approximation , 6 2 subspace, 1 theta function , 241fT . totally isotropic , 2 unipotent radical , 10 , 68 weak approximation , 6 5 weight, 7 8 Witt decomposition , 4 , 26 weak, 4 , 26 Witt's theorem , 2
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