Siegel Modular Forms A Classical and Representation-Theoretic Approach /

• Main Author: Pitale, Ameya (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Mathematics, 2240
• Subjects: Number theory.; Group theory.; Number Theory.; Group Theory and Generalizations.

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 im...

Table of Contents:

• Introduction
• Lecture 1:Introduction to Siegel modular forms
• Lecture 2: Examples
• Lecture 3: Hecke Theory and L-functions
• Lecture 4: Non-vanishing of primitive Fourier coefficients and applications
• Lecture 5: Applications of properties of L-functions
• Lecture 6: Cuspidal automorphic representations corresponding to Siegel modular forms
• Lecture 7: Local representation theory of GSp4(ℚp)
• Lecture 8: Bessel models and applications
• Lecture 9: Analytic and arithmetic properties of GSp4 x GL2 L-functions
• Lecture 10: Integral representation of the standard L-function.