This is Anil Aryasomayajula's talk "What is ... a Modular form?" at the "What is ...?" seminar. The talk was given on Friday, April 15, 2011, 11:45am at the BMS Loft at Urania.
Modular forms are complex analytic functions on the upper half plane satisfying a certain kind of functional equation and growth condition. In this talk we see how the theory of modular forms answers a classical problem in number theory, namely: "Which natural numbers can be represented as the sum of four squares, and in how many ways can that be done."
For more "What is ...?" seminar videos, visit math.fu-berlin.de/w/Math/WhatIsSeminar.