Math 205B: Number Theory, Winter 2022

Introduction to automorphic forms and representations

Mon, Wed, Fri 12-12:50pm
Math Sciences Building 7608; Zoom 952 7871 8805, Passcode: 205

Instructor
Chi-Yun Hsu
Email: cyhsu at math.ucla.edu
Office: MS 5242
Office Hour: Mondays 1-2pm

Grade
Homework 100%

Tentative plan
Week 1-3: Automorphic forms of GL(1) - Dirichlet characters, Dirichlet L-functions, analytic continuation and functional equation. Adelic language, Fourier analysis and Tate's thesis.
Week 4-10: Automorphic forms of GL(2) - Modular forms, L-functions and properties. Automorphic forms and representations. Local theory. Rankin-Selberg method and converse theorem.

References
GL(1):

• Bump, Automorphic forms and representations, 1.1, 3.1
• Cassels and Frolich, Algebraic Number Theory, Chapter XV
• Ramakrishnan and Valenza, Fourier Analysis on Number Fields

• Bump, Automorphic forms and representations