TABLE OF CONTENTS
Preface vii
Notation and Terminology ix
Introduction 1
Chapter I. MULTIPLE GAMMA FUNCTION AND ITS GENERALIZA-
TIONS 13
§1. Basic integral representations 13
§2. Shintani's formulas 17
§3. The second derivative of £(s, A, x) at s = 0 24
§4. An asymptotic expansion of the multiple gamma function 34
Exercises 41
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
§4. An example 54
Exercises 58
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
Exercises 133
Chapter IV. EXPLICIT CONE DECOMPOSITIONS AND APPLICA-
TIONS 135
§1. A special decomposition of a higher dimensional cube 135
§2. Topological preparations 139
§3. A sufficient condition for a cone decomposition 144
§4. Examples 147
§5. Explicit cone decompositions for index finite subgroups 149
§6. Applications 161
Exercises 166
Previous Page Next Page