Automorphic Forms

Fall 2018

The seminar will meet weekly at the Student Lounge or Thesis Room, from 4:00pm-5:00pm on Friday. The official homepage for the seminar is here.

I will be talking about various aspect of classical modular forms, especially its application in number theory. My first goal is to give you a fundamental treatment of modular forms, a first course if you will (which mean that it comes with little pre-requisite and could be viewed as a typical graduate course like algebraic topology).

The (incomplete list of) topics I want to talk about are:

Along the way, I shall review some topic such as Riemann surfaces, sheaf and algebraic geometry.

Unlike last semester, I shall upload the combined note when I think they are ready.

Here is Kindle version of William Stein's book Modular Forms: A Computational Approach that I recompiled from his TeX source code.

This time, I make all my notes in Kindle size.

Modular Forms I

September 7th, 2018

Abstract: Definition of modular forms, examples, classification of linear fractional transformations

Modular Forms II

September 14th, 2018

Abstract: Absolute convergence of Eisenstein series (missing from last time), cusps, elliptic points, Fourier expansion

Modular Forms III

September 21st, 2018

Abstract: Review of Riemann surfaces: the category of Riemann surfaces, uniformization theorem, compact Riemann surfaces, differentials

Modular Forms IV

September 28st, 2018

Abstract: Modular curves as Riemann surfaces, interpretation of modular forms as differential on modular curves

Modular Forms V

October 5th, 2018

Abstract: Dimension formulas for the space of modular forms

Modular Forms VI

October 12th, 2018

Abstract: Dimension formulas for the space of modular forms (Continued)

Modular Forms VII

October 19th, 2018


Modular Forms VIII

October 26th, 2018

Abstract: Hecke operators

Modular Forms IX

October 26th, 2018

Abstract: Primitive forms

Modular Forms X

November 2nd, 2018