Quantum modular forms have emerged as a versatile framework that bridges classical analytic number theory with quantum topology and mathematical physics. Initially inspired by the pioneering work on ...

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 ...

We present an asymptotically fast algorithm for the numerical evaluation of modular functions such as the elliptic modular function j. Our algorithm makes use of the natural connection between the ...

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 ...

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 ...