Introduction to Modular Forms

2014/07/04 by Simon Rose, Rose, Simon
Mathematics · #11F11 #11F37 #14N10 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F37 #msc:14N10

paper · pdf · doi:10.48550/arxiv.1407.1262

22 Pages

arxiv created 2014/07/04 · arxiv updated 2014/07/07

Abstract

We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes are based on a lecture given at the Field's institute during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.

Related

• Lectures on modular forms and strings
• Hilbert modular forms and their applications
• Computational Arithmetic of Modular Forms (Course notes)
• Algebraic topology and modular forms
• Generalized modular forms including the weak Maass forms,the Ramanujan's Theta functions and the Tau function