Number theory II.a - Modular forms

Summary

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

Content

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Keywords

Modular forms, Modular group, linear frantional transformations, theta functions

Learning Prerequisites

Required courses

Complex analysis

Fourier analysis

Recommended courses

Algebraic topology, classification of comp[act surfaces

Assessment methods

Oral

Resources

Bibliography

1. A first course in modular forms. Fred Diamond; Jerry Shurman; 2005
2. The 1-2-3 of modular forms : lectures at a summer school in Nordfjordeid, Norway. Don Zagier; 2008
3. Topics in Classical Automorphis forms. Henryc Iwaniec

Ressources en bibliothèque

• A first course in modular forms / Diamond
• Topics in classical automorphic forms / Iwaniec
• The 1-2-3 of modular forms / Zagier

Moodle Link

• https://go.epfl.ch/MATH-511