From Tate's zeta-integral to Eisenstein series (An introduction to the analytic and spectral theory of automorphic representations)
Student No.:50
Time:Tue/Thu 10:10-12:00, 2016-09-08~ 2016-12-29 (No classes on public holidays)
Instructor:Han Wu  [Eidgenössische Technische Hochschule Zürich]
Place:Conference room 4, floor 2, Jin Chun Yuan West Building
Starting Date:2016-9-8
Ending Date:2016-12-29






The course will be composed with two parts.



The first part consists of an introduction to the theory of algebraic numbers, with emphasis on the analytic theory and adelic treatment. This part ends with Tate's thesis.



The second part consists of an introduction to the analytic theory of smooth Eisenstein series, realized as “two-dimensional” zeta-integrals. We would like to open the doors for:



- the spectral theory of automorphic representations


- the theory of Jacquet-Langlands'correspondence


- Zagier's regularized integral theory.


The transition between classical and adelic descriptions will be detailed.






We will try the best to make the course accessible to undergraduate students on the second year. Knowledge beyond this scope from algebra and geometry will be recalled without proof but with references. Knowledge beyond this scope from analysis will be treated as detailedly as the audience demands.




Reference for the course:


- S.Lang: Algebraic Number Theory, Second Edition. GTM 110. Springer-Verlag, 2003


- H.Wu: “Burgess-like subconvexity for $GL_1$”,

For further reading:


- S.S.Gelbart: Automorphic Forms on Adele Groups. Princeton University Press and University of Tokyo Press, 1975


- S.S.Gelbart and H.Jacquet: “Forms of GL(2) from the analytic point of view” in Automorphic forms, representations and L-functions, Part I (Proc.Sympos.Pure Maht., Oregon State Univ., Corvallis, Ore. 1977), 213-251, Am.Math.Soc., Providence, 1979


- H.Jacquet and R.P.Langlands: Automorphic Forms on GL(2). Lecture Notes in Mathematics: 114. Springer-Verlag, 1970