Dimension Formulae for the Vector Spaces of Siegel Cusp Forms of Degree Three.

Intro -- TABLE OF CONTENTS -- LIST OF NOTATIONS -- INTRODUCTION -- CHAPTER I: FIXED POINTS AND CONJUGACY OF REGULAR ELLIPTIC ELEMENTS IN Sp(3, Z) -- 1.1 Introduction -- 1.2 Notations and basic results -- 1.3 Reducible cases -- 1.4 Symplectic embeddings of Q(e[(2πi/9)]) and Q(e[(2πi/7)]) -- 1.5 Application -- CHAPTER II: CONJUGACY CLASSES OF THE MODULAR GROUP Sp(3, Z) -- 2.1 Introduction -- 2.2 Basic results -- 2.3 Conjugacy classes of Γ[sup(2)][sub(3)] -- 2.4 Conjugacy classes of Γ[sup(1)][sub(3)] -- 2.5 Conjugacy classes of Γ[sup(3)][sub(0)] -- 2.6 Applications and further remarks -- CHAPTER III: EXPLICIT EVALUATIONS -- 3.1 Introduction -- 3.2 Contributions from conjugacy classes of regular elliptic elements -- 3.3 Contribution from conjugacy classes in Γ[sup(2)][sub(3)] -- 3.4 Contributions from conjugacy classes in Γ[sup(1)][sub(3)] -- 3.5 Contributions from conjugacy classes in Γ[sup(0)][sub(3)] -- 3.6 An explicit dimension formula for Siegel cusp forms of degree three -- 3.7 Autemorphic forms of degree three and its generating function -- CHAPTER IV: DIMENSION FORMULAE FOR THE VECTOR SPACES OF SIEGEL CUSP FORMS OF DEGREE THREE -- 4.1 Introduction -- 4.2 Eie's results -- 4.3 Conjugacy classes of Sp(3, Z) -- 4.4 The main terms -- 4.5 Determination of C[sub(1)], C[sub(2)] and C[sub(3)] -- 4.6 The partial fractions of the generating function -- 4.7 The generating function for modular form of degree four -- REFERENCES.

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