CONTENTS

Chapter VI. Analytic Continuation and Near Holomor-

phy of Eisenstein Series of General Types 185

23. Eisenstein series of general types 185

24. Pullback of Eisenstein series 194

25. Proof of Theorems in Sections 20 and 23 203

26. Near holomorphy of Eisenstein series in Case UB 208

Chapter VII. Arithmeticity of the Critical Values of

Zeta Functions and Eisenstein Series of General Types 219

27. The spaces of holomorphic Eisenstein series 219

28. Main theorems on arithmeticity in Cases SP and UT 230

29. Main theorems on arithmeticity in Case UB 240

Appendix 247

Al. The series associated to a symmetric matrix and Gauss

sums 247

A2. Metaplectic groups and factors of automorphy 251

A3. Transformation formulas of general theta series 262

A4. The constant term of a theta series at each cusp depends

only on the genus 272

A5. Theta series of a hermitian form 274

A6. Estimate of the Fourier coefficients of a modular form 278

A7. The Mellin transforms of Hilbert modular forms 282

A8. Certain unitarizable representation spaces 285

References 297

Index

301