MIXED AUTOMORPHIC FORMS, TORUS BUNDLES, AND JACOBI FORMS

By JESSICA BROWN

CONTENTS INTRODUCTION MIXED AUTOMORPHIC FORMS MIXED AUTOMORPHIC FORMS OF ONE VARIABLE EISENSTEIN SERIES AND POINCAR´E SERIES CUSP FORMS ASSOCIATED TO MIXED CUSP FORMS MIXED AUTOMORPHIC FORMS AND DI?ERENTIAL EQUATIONS LINE BUNDLES AND ELLIPTIC VARIETIES MIXED CUSP FORMS AND LINE BUNDLES ELLIPTIC VARIETIES MODULAR SYMBOLS EICHLER-SHIMURA RELATIONS MIXED AUTOMORPHIC FORMS AND COHOMOLOGY MIXED CUSP FORMS AND PARABOLIC COHOMOLOGY PAIRINGS ON MIXED CUSP FORMS HODGE STRUCTURES THE KRONECKER PAIRING MIXED HILBERT AND SIEGEL MODULAR FORMS MIXED HILBERT MODULAR FORMS FAMILIES OF ABELIAN VARIETIES OVER HILBERT MODULAR VARIETIES MIXED SIEGEL MODULAR FORMS FOURIER COE?CIENTS OF SIEGEL MODULAR FORMS MIXED AUTOMORPHIC FORMS ON SEMISIMPLE LIE GROUPS MIXED AUTOMORPHIC FORMS ON SYMMETRIC DOMAINS EISENSTEIN SERIES WHITTAKER VECTORS FOURIER COE?CIENTS OF EISENSTEIN SERIES FAMILIES OF ABELIAN VARIETIES KUGA FIBER VARIETIES AUTOMORPHY FACTORS AND KERNEL FUNCTIONS MIXED AUTOMORPHIC FORMS AND KUGA FIBER VARIETIES EMBEDDINGS OF KUGA FIBER VARIETIES JACOBI FORMS JACOBI FORMS ON SYMMETRIC DOMAINS FOCK REPRESENTATIONS THETA FUNCTIONS VECTOR-VALUED JACOBI FORMS TWISTED TORUS BUNDLES TWO-COCYCLES OF DISCRETE GROUPS ONE-COCHAINS ASSOCIATED TO 2-COCYCLES FAMILIES OF TORUS BUNDLES COHOMOLOGY REFERENCES