ON SHIMURA'S CORRESPONDENCE FOR MODULAR FORMS OF HALF-INTEGRAL WEIGHT*......Page 11
The Metaplectic Group......Page 14
Admissible Representations......Page 16
Whittaker Models......Page 18
The Theta-Representations r......Page 20
A Functional Equation of Shimura Type......Page 22
L and -Factors......Page 24
A Local Shimura Correspondence......Page 27
The Metaplectic Group......Page 29
Automorphic Representations of Half-Integral Weight......Page 30
Fourier Expansions......Page 31
Theta-Representations......Page 35
A Shimura-Type Zeta Integral......Page 36
An Euler Product Expansion......Page 39
The Theorem......Page 44
Applications and Concluding Remarks......Page 49
PERIOD INTEGRALS OF COHOMOLOGY CLASSESWHICH ARE REPRESENTED BY EISENSTEIN SERIES......Page 56
The Eisenstein Series......Page 86
Arithmetic Applications......Page 128
Generalities......Page 141
Examples......Page 154
ON P-ADIC REPRESENTATIONS ASSOCIATED WITH Zp-EXTENSIONS......Page 167
Introduction......Page 181
Maass forms......Page 182
Fourier expansions......Page 183
The Mellin Transform......Page 185
The convolution......Page 186
Functional Equations......Page 189
CRYSTALLINE COHOMOLOGY, DIEUDONNรMODULES, AND JACOBI SUMS......Page 192
ESTIMATES OF COEFFICIENTS OF MODULARFORMS AND GENERALIZED MODULAR RELATIONS......Page 282
A REMARK ON ZETA FUNCTIONS OF ALGEBRAICNUMBER FIELDS1......Page 291
Complex quadratic ground fields......Page 298
L-series considered over Q......Page 306
EISENSTEIN SERIES AND THE RIEMANNZETA-FUNCTION......Page 312
Introduction......Page 342
Statement of the main theorem......Page 346
Eisenstein series and the spectral decomposition.........Page 352
Computation of I(s) for (s) >1.......Page 363
Analytic continuation of I(s),......Page 374