Index a, 9 Ak, 32 Au,, 32 b, 30 deti(x), 91 e a , 10, 32 e A i e h ) e p e v i 10 127 e£,32 g±Ti f^n ~n G JL » e h ' e v G, 20 Go, 21 G+, 54 0-lattice, 9 n , 135 h, 9 H C M , 76 il3(x), 12 j*(z), 19, 30 j f c , 130 J K , 77 [A ], 130 /CQ, 58 £ (field), 47 £ (group), 110 £o, 89 M(a,z), 26, 30 M/ p ( , ), 89 •Mfc,31 Ml, 208 Mu, 31 9K, 129, 254 v{x), 11 ^o(x), 10 MO, 161 py(a,/3), 78 p(w), 78 ¥*(*), 82 SP{ , ), 89 5^, 35, 208 S*, 208 5^,3 4 X(s,f,X), 173 il, 285 v, 9 Z £ , 5 0 Z(s, f,x), 173, 176 3^,208 abelian variety, 13 adelization, 9 anisotropic, 7 automorphic form, 32 automorphic function, 32 canonical model, 58 Case SP, 17 Case UB, 17 Case UT, 17 CM-algebra, 17 CM-field, 12 CM-type, 12 component of an automorphic form, 166 congruence subgroup, 27 cusp condition, 33, 103 cusp form, 34, 73 denominator ideal, 10 factor of automorphy, 18, 19 factor of automorphy of weight 1/2, 40, 254 field of moduli, 16 Gauss sum, 156 generic, 46 half-integral weight, 41 Hecke character, 129 integral weight, 41 involution of the endomorphism algebra, 15 isotropic, 7 lattice in a real vector space, 13 Mobius function, 163 metaplectic group, 252 modular form, 32 modular form of half-integral weight, 41 nearly holomorphic function, 100 PEL-type, 23 period symbol, 77 polarization, 14 polarized abelian variety, 14 301
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