Book Review: Modular forms

Harmonic Maass Forms, Mock Modular Forms, and Quantum Modular Forms

This short course is an introduction to the theory of harmonic Maass forms, mock modular forms, and quantum modular forms. These objects have many applications: black holes, Donaldson invariants, partitions and q-series, modular forms, probability theory, singular moduli, Borcherds products, central values and derivatives of modular L-functions, generalized Gross-Zagier formulae, to name a few....

Book Review

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Modular Forms

Here are the notes I took for Wei Zhang’s course on modular forms offered at Columbia University in Spring 2013 (MATH G4657: Algebraic Number Theory). Hopefully these notes will appear in a more complete form during Fall 2014. I recommend that you visit my website from time to time for the most updated version. Due to my own lack of understanding of the materials, I have inevitably introduced b...

Modular Functions and Modular Forms

These are the notes for Math 678, University of Michigan, Fall 1990, exactly as they were handed out during the course except for some minor revisions and corrections. Please send comments and corrections to me at [email protected].

Book Review