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Dimensions of Spaces of Siegel Cusp Forms of Degree Two and Three.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1984Copyright date: ©1984Edition: 1st edDescription: 1 online resource (194 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470407179
Subject(s): Genre/Form: Additional physical formats: Print version:: Dimensions of Spaces of Siegel Cusp Forms of Degree Two and ThreeDDC classification:
  • 512/.72
LOC classification:
  • QA3 -- .E34 1984eb
Online resources:
Contents:
Intro -- TABLE OF CONTENTS -- LIST OF NOTATIONS -- INTRODUCTION -- CHAPTER I: CONJUGACY CLASSES OF Sp (2 , Z) -- 1.1 Introduction -- 1.2 Representatives of conjugacy classes of finite order elements -- 1.3 Conjugacy classes of finite order elements in Sp (2 , Z) -- 1.4 Conjugacy classes of Γ1[sup(∞)] -- 1.5 Conjugacy classes of Γ0[sup(∞)] -- CHAPTER II: DIMENSION FORMULA FOR THE VECTOR SPACE OF CUSP FORMS OF DEGREE TWO WITH RESPECT TO Sp (2 , Z) -- 2.1 Introduction -- 2.2 Contributions from elliptic conjugacy classes -- 2.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (I) -- 2.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (II) -- 2.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points -- 2.6 Contributions from conjugacy classes of unipotent elements -- 2.7 A dimension formula for the vector space of cusp forms with respect to Sp (2 , Z) -- CHAPTER III: REPRESENTATIVES OF CONJUGACY CLASSES OF ELEMENTS OF Sp (3 , Z) IN Sp (3 , R) -- 3.1 Introduction -- 3.2 Conjugacy classes of torsion elements in Sp (3 , Z) -- 3.3 A classification of conjugacy classes of Sp (3 , Z) -- 3.4 Selberg's trace formula and its modification -- 3.5 Conjugacy classes with zero contribution (I) -- 3.6 Conjugacy classes with zero contribution (II) -- CHAPTER IV: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Δ ∪ Δ[sub(1)] ∪ Δ[sub(2)] ∪ Δ[sub(0)] -- 4.1 Introduction -- 4.2 Contributions from elliptic conjugacy classes -- 4.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points -- 4.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points -- 4.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points.
4.6 Second case of conjugacy classes of elements having a one-dimensional set of fixed points -- 4.7 Second case of conjugacy classes of elements having a two-dimensional set of fixed points -- CHAPTER V: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Δ[sub(0)] -- 5.1 Introduction -- 5.2 A dimension formula for the principal congruencesubgroup Γ[sub(2)](N) -- 5.3 Contributions from Δ[sub(0)](I) -- 5.4 A dimension formula for the principal congruence subgroup Γ[sub(3)](N) -- 5.5 Contributions from Δ[sub(0)](II) -- 5.6 A final remark -- REFERENCES.
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Intro -- TABLE OF CONTENTS -- LIST OF NOTATIONS -- INTRODUCTION -- CHAPTER I: CONJUGACY CLASSES OF Sp (2 , Z) -- 1.1 Introduction -- 1.2 Representatives of conjugacy classes of finite order elements -- 1.3 Conjugacy classes of finite order elements in Sp (2 , Z) -- 1.4 Conjugacy classes of Γ1[sup(∞)] -- 1.5 Conjugacy classes of Γ0[sup(∞)] -- CHAPTER II: DIMENSION FORMULA FOR THE VECTOR SPACE OF CUSP FORMS OF DEGREE TWO WITH RESPECT TO Sp (2 , Z) -- 2.1 Introduction -- 2.2 Contributions from elliptic conjugacy classes -- 2.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (I) -- 2.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (II) -- 2.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points -- 2.6 Contributions from conjugacy classes of unipotent elements -- 2.7 A dimension formula for the vector space of cusp forms with respect to Sp (2 , Z) -- CHAPTER III: REPRESENTATIVES OF CONJUGACY CLASSES OF ELEMENTS OF Sp (3 , Z) IN Sp (3 , R) -- 3.1 Introduction -- 3.2 Conjugacy classes of torsion elements in Sp (3 , Z) -- 3.3 A classification of conjugacy classes of Sp (3 , Z) -- 3.4 Selberg's trace formula and its modification -- 3.5 Conjugacy classes with zero contribution (I) -- 3.6 Conjugacy classes with zero contribution (II) -- CHAPTER IV: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Δ ∪ Δ[sub(1)] ∪ Δ[sub(2)] ∪ Δ[sub(0)] -- 4.1 Introduction -- 4.2 Contributions from elliptic conjugacy classes -- 4.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points -- 4.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points -- 4.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points.

4.6 Second case of conjugacy classes of elements having a one-dimensional set of fixed points -- 4.7 Second case of conjugacy classes of elements having a two-dimensional set of fixed points -- CHAPTER V: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Δ[sub(0)] -- 5.1 Introduction -- 5.2 A dimension formula for the principal congruencesubgroup Γ[sub(2)](N) -- 5.3 Contributions from Δ[sub(0)](I) -- 5.4 A dimension formula for the principal congruence subgroup Γ[sub(3)](N) -- 5.5 Contributions from Δ[sub(0)](II) -- 5.6 A final remark -- REFERENCES.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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