Math 687R, Spring 2016

Homework problems

Instructor:  Paul Jenkins
Office:  282 TMCB, 801-422-5868
Email:  jenkins@math.byu.edu
Lecture:  1:30-3:30 TTh, 11:00-11:50 W, 292 TMCB
Office hours:  By appointment
Textbook:  Modular forms: a classical and computational introduction, 2nd edition, L.J.P. Kilford, Imperial College Press, ISBN 978-1-78326-545-9.

• Modular forms: a computational approach, William Stein
• The 1-2-3 of modular forms, Bruinier-van der Geer-Harder-Zagier
• A first course in modular forms, Diamond-Shurman.

Grading:  Homework 50%, presentations 50%.
Homework:  Homework will be due at 4:30 PM in the box outside my office on Tuesdays and Fridays.  Homework assignments will be posted on the course website. Late homework will not be accepted.  Working in groups on homework is encouraged, but each student should write up each problem, without looking at other students’ written solutions.

Here is an incomplete list of papers that would be appropriate for class presentations:

• Rankin and Swinnerton-Dyer, On the zeros of Eisenstein series, BLMS 1970
• Ghosh and Sarnak, Real zeros of holomorphic Hecke cusp forms, Jour. Eur. Math Soc. 2012
• Zagier, Traces of singular moduli
• Ahlgren, Masri, and Rouse, Vanishing of modular forms at infinity, PAMS 2009
• Viazovska, The sphere packing problem in dimension 8 (see this article)
• El-Guindy, Fourier expansions with modular form coefficients, IJNT 2009
• Rouse and Webb, Spaces of modular forms spanned by eta-quotients, Advances in Mathematics 2015

Learning Outcomes: See the Math 675R or Math 687R pages on the BYU math website.

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