Math 8280: Topics in Number Theory (2019--2020)

Instructor:

  • Dr. Dihua Jiang
  • Office: VinH 224, Telephone: 625-7532, E-mail: jiang034@umn.edu

    Lectures:

  • Lecture: 2:30--3:20pm, MWF at Vincent Hall 206 (Office Hours: by appointment)

    Course Description:


    This is a two-semester course for Automorphic L-functions and related topics in the Langlands Program.

    The Langlands functoriality conjecture is a profound core conjecture in the Langlands program, which
    is also the name for the modern theory of automorphic forms. Automorphic L-functions are intrinsic invariants
    attached to a given automorphic forms or representations, which also serve as bridges connecting the modern
    theory of automorphic forms to number theory, algebraic geometry, representation theory and harmonic analysis
    over certain locally compact topological spaces.

    In this one-year long course, the following topics will be covered:

    1) Automorphic Forms on GL(n);

    2) Automorphic L-functions of GL(n): analytic properties and zeta integrals;

    3) Basics on Eisenstein series: Langlands-Shahidi method, possible generalization;

    4) Analytic Properties of Automorphic L-functions and Langlands Functorial Transfers;

    5) Arithmetic Properties of Automorphic L-functions.

    Basic reference:
    1) Moeglin and Waldspurger: Spectral Decomposition and Eisenstein Series. Cambridge University Press, 1995.
    2) Arthur: The Endoscopy Classification of Representations: orthogonal and symplectic groups. AMS Colloquium 61, 2013.
    3) Some relevant research papers.
    4) Shahidi: Eisenstein series and automorphic L-functions.

    Homework and Exams:
    Homework Problems will be assigned, but no exams are required. Students may give reports to the class.