TABLE OF CONTENTS
LIST OF NOTATIONS V
INTRODUCTION •• •• 1
CHAPTER I CONJUGACY CLASSES OF Sp(2, Z) 7
1.1 Introduction 7
1.2 Representatives of conjugacy classes of finite
order elements 8
1.3 Conjugacy classes of finite order elements in
Sp(2,Z) •• , 11
1.4 Conjugacy classes of Ti 14
1.5 Conjugacy classes of r0°° 17
CHAPTER II DIMENSION FORMULA FOR THE VECTOR SPACE OF CUSP
FORMS OF DEGREE TWO WITH RESPECT TO Sp(2,Z) ••• 21
2 .1 Introduction 21
2.2 Contributions from elliptic conjugacy classes •• 22
2.3 Contributions from conjugacy classes of elements
having a one-dimensional set of fixed points (I) 23
2.4 Contributions from conjugacy classes of elements
having a one-dimensional set of fixed points (H) 30
2.5 Contributions from conjugacy classes of elements
having a two-dimensional set of fixed points ••• 37
2.6 Contributions from conjugacy classes of unipotent
elements * 43
2.7 A dimension formula for the vector space of cusp
forms with respect to Sp(2,Z) •• 44
CHAPTER III REPRESENTATIVES OF CONJUGACY CLASSES OF ELEMENTS
OF Sp(3,Z) IN Sp(3,R) 46
3 .1 Introduction 46
3.2 Conjugacy classes of torsion elements in
Sp(3,Z) •••• 47
3.3 A classification of conjugacy classes of
Sp(3,Z) •••» 51
3.4 Selberg's trace formula and its modification ••• 56
3.5 Conjugacy classes with zero contribution (I) ••• 62
3.6 Conjugacy classes with zero contribution (IE) ••• 66
CHAPTER IV CONTRIBUTIONS FROM CONJUGACY CLASSES IN
All A1 U A2 U A0 ** * 81
4 .1 Introduction » 81
4.2 Contributions from elliptic conjugacy classes •• 82
4.3 Contributions from conjugacy classes of elements
having a one-dimensional set of fixed points ••• 86
4.4 Contributions from conjugacy classes of elements
having a one-dimensional set of fixed points ••• 97
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