Modular forms provide a powerful mathematical framework for understanding symmetry in two-dimensional quantum field theories. In conformal field theory (CFT), these holomorphic functions obey ...

American Journal of Mathematics, Vol. 138, No. 3 (June 2016), pp. 821-878 (58 pages) Let f be a modular form of weight k and Nebentypus ψ. By generalizing a construction of Dabrowski and Delbourgo, we ...

“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...

Sage codes for computations related to quantum modular forms, mostly plotting "error functions". Examples from the following papers are covered: Zagier, D., "Quantum ...

In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last Theorem, a central problem in number theory that had remained open ...

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...