Modular Forms: A Classical Approach
β Henri Cohen, Fredrik StrΓΆmberg
π Library
π
2017
π American Mathematical Society
π English
β¦ LIBER β¦
π
Siegel Modular Forms: A Classical and Representation-Theoretic Approach
β Scribed by Ameya Pitale
- Publisher
- Springer International Publishing
- Year
- 2019
- Tongue
- English
- Leaves
- 142
- Series
- Lecture Notes in Mathematics 2240
- Edition
- 1st ed.
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation.
Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
β¦ Table of Contents
Front Matter ....Pages i-ix
Introduction to Siegel Modular Forms (Ameya Pitale)....Pages 1-7
Examples (Ameya Pitale)....Pages 9-14
Hecke Theory and L-Functions (Ameya Pitale)....Pages 15-22
Nonvanishing of Fourier Coefficients and Applications (Ameya Pitale)....Pages 23-29
Applications of Properties of L-Functions (Ameya Pitale)....Pages 31-37
Cuspidal Automorphic Representations Corresponding to Siegel Modular Forms (Ameya Pitale)....Pages 39-48
Local Representation Theory of (\mathrm{GSp}_4({\mathbb Q}_p)) (Ameya Pitale)....Pages 49-62
Bessel Models and Applications (Ameya Pitale)....Pages 63-74
Analytic and Arithmetic Properties of (\mathrm{GSp}_4 \times \mathrm{GL}_2)L-Functions (Ameya Pitale)....Pages 75-82
Integral Representation of the Standard L-Function (Ameya Pitale)....Pages 83-91
Back Matter ....Pages 93-138
β¦ Subjects
Mathematics; Number Theory; Group Theory and Generalizations
π SIMILAR VOLUMES
Classical Theorems in Lie Algebra Repres
β Whitman, Andrew P., S.J. & Lutts, John A.
π Library
π
2013
π Vatican Observatory & University of Massachusetts
π English
Theoretical Physics: A Classical Approac
β Professor Dr. Josef Honerkamp, Professor Dr. Hartmann RΓΆmer (auth.)
π Library
π
1993
π Springer-Verlag Berlin Heidelberg
π English
<p>This introduction to classical theoretical physics emerged from a course for students in the third and fourth semester, which the authors have given several times at the University of Freiburg (Germany). The goal of the course is to give the student a comprehensive and coherent overview of the pr
Theoretical Approaches in Psychology (Ap
β Matt Jarvis
π Library
π
2000
π English
Psychologists use a range of principles and theories, all of which view the person and the study of the person in very different ways. Theoretical Approaches in Psychology introduces and outlines the six main approaches and considers how each has helped psychologists understand human behaviour, thou
Modular Forms: A Classical and Computati
β Lloyd Kilford
π Library
π
2008
π World Scientific Pub Co (
π English
This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quad
Modular forms: A classical and computati
β Lloyd Kilford
π Library
π
2008
π Imperial College Press
π English
This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quad