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 ...

Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL₂(Z) in terms of the values of modular functions at points ...

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 ...

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 ...

PROOFS are the currency of mathematics, but Srinivasa Ramanujan, one of the all-time great mathematicians, often managed to skip them. Now a proof has been found for a connection that he seemed to ...