Automorphic L-functions lie at the confluence of number theory, harmonic analysis and representation theory. These functions generalise the classical Riemann zeta function and are constructed from ...

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 a novel integral representation for a quotient of global automorphic 𝐿-functions, the symmetric square over the exterior square. The pole of this integral characterizes a period of a ...

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism. In 2018, as he prepared to be awarded the Fields Medal, math’s highest ...