Absolute CM-periods / Hiroyuki Yoshida.

Format:

Book

Author/Creator:

Yoshida, Hiroyuki, 1947-

Series:

Mathematical surveys and monographs ; no. 106.

Mathematical surveys and monographs, 0076-5376 ; v. 106

Language:

English

Subjects (All):

Abelian varieties.

Automorphic forms.

Functions, Zeta.

Physical Description:

x, 282 pages ; 27 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2003]

Contents:

Chapter I. Multiple Gamma Function and Its Generalizations 13

1. Basic integral representations 13

2. Shintani's formulas 17

3. The second derivative of [zeta](s, A, x) at s = 0 24

4. An asymptotic expansion of the multiple gamma function 34

Chapter II. The Stark-Shintani Conjecture 43

1. Stark's general conjecture 43

2. Transition to a more precise conjecture 48

3. Shintani's formulas for the partial zeta function 52

Chapter III. Absolute CM-periods 61

1. Shimura's period symbol pk 61

2. The case of abelian fields 65

3. Conjectures on absolute CM-periods 74

4. Numerical examples 94

5. Further investigations on the invariant X(c) 108

6. Numerical examples (continued) 126

Chapter IV. Explicit Cone Decompositions and Applications 135

1. A special decomposition of a higher dimensional cube 135

2. Topological preparations 139

3. A sufficient condition for a cone decomposition 144

5. Explicit cone decompositions for index finite subgroups 149

6. Applications 161

Chapter V. Applications of a Limit Formula of Kronecker's Type 169

1. A limit formula of Kronecker's type 169

2. A generalization of the exact Chowla-Selberg formula 179

3. L-functions of orders of an algebraic number field 189

4. Toward the reciprocity law for the h-function 197

5. A connection of automorphic forms with group cohomology 207

Appendix I. Eisenstein Series on GL(2) 215

1. Eisenstein series on GL(2) 215

2. Calculations of local integrals 222

3. The functional equation of Eisenstein series 234

4. Eisenstein series of class 1 243

Appendix II. On Higher Derivatives of L-Functions 249

1. A search for new invariants 249

2. The case of the second derivatives of L-functions 253

Appendix III. Transcendental Property of CM-periods 269.

Notes:

Includes bibliographical references (pages 275-279) and index.

ISBN:

0821834533

OCLC:

52945971