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Theta Functions from an Analytic Viewpoint
Plancherel Theorem for R
The Group AX
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algebraic apply an induction arbitrary element arbitrary point assume automorphy factor bicontinuous isomorphism biholomorphic C-base C-linear mapping canonical base Chap closed set commutative complete set complex manifold connected const contained convergent defined degree g denote an arbitrary denote an element dimension exists an element finite number graded ring Gz(e Haar measure hence holomorphic function holomorphic mapping homogeneous implies integral domain irreducible isomorphism kernel lattice Lemma Lemma 12 Let X denote linear locally compact group modular forms monoid Moreover multiplication non-degenerate normal notation observe open neighborhood open subset PN(C polarized abelian variety positive divisor positive integer positive-definite projective embedding projective variety prove quotient recall reK2 rg(l Riemann form satisfying sequence set of representatives Sp(X subring subspace Suppose surjective symmetric theta constants theta function topology unique unitary representation vector space Weierstrass polynomial Zariski closed set zero