Modular Forms

Notes for Advanced Number Theory (Master in Advanced Mathematics, UAB/UB)

Preface

These are notes used by the author on part of a course on Advanced Number Theory taught at UB/UAB during Spring 2024. They evolved from a course on Modular Forms taught at the University of Warwick during autumn of 2015, and are based on a variety of sources, mainly:

1. The books Diamond and Shurman (2005) and Serre (2012) listed in the bibliography.
2. Notes from a course taught by Peter Bruin in the spring term of 2014, which in turn are based on
3. Notes from a course taught by David Loeffler in the autumn term of 2011;
4. Notes from a course taught by Scott Ahlgren (UIUC) in 2006.

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Diamond, Fred, and Jerry Michael Shurman. 2005. A First Course in Modular Forms. Vol. 228. Springer.

Serre, Jean-Pierre. 2012. A Course in Arithmetic. Vol. 7. Springer Science & Business Media.