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 ...

This book presents a treatment of the theory of L-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands ...

A new mathematical object, long know to exist but never seen, had its first sighting yesterday. Two researchers have exhibited the first example of a third degree transcendental L-function. These ...

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 ...

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 ...

Prime numbers are maddeningly capricious. They clump together like buddies on some regions of the number line, but in other areas, nary a prime can be found. So number theorists can’t even roughly ...