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 ...

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 ...

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 ...