In this talk I will construct a class of probabilistic random
Euler products to model the behavior of L-functions in the strip
1/2 Re(s) 1. We then deduce results on the distribution of extreme
values of several families of L-functions, including...
We describe how various fundamental algebraic structures
(involving, for example, number fields, class groups, and algebraic
curves) can be parameterized via the orbits of appropriate group
representations. By developing techniques to count such...
Let E be an elliptic curve over Q and let Q(E[n]) be its n-th
division field. In 1972, Serre showed that if E is without complex
multiplication, then the Galois group of Q(E[n])/Q is as large as
possible, that is, GL_2(Z/n Z), for all integers n...
We describe how various fundamental algebraic structures
(involving, for example, number fields, class groups, and algebraic
curves) can be parameterized via the orbits of appropriate group
representations. By developing techniques to count such...
I first present an algorithm to compute the truncated theta
function in poly-log time. The algorithm is elementary and suited
for computer implementation. The algorithm is a consequence of the
periodicity of the complex exponential, and the self...
Let K/Q be an extension of number fields. The Hasse norm theorem
states that when K is cyclic any non-zero element of Q can be
represented as a norm from K globally if and only if it can be
represented everywhere locally. In this talk I will discuss...
We discuss the question of quantitative bounds on the sup-norm
of automorphic cusp forms. We present an improvement on a recent
result by Blomer-Holowinsky on Hecke-Maass forms on $X_0(N)$ with
large level $N$. Analogous results are then established...
In this joint work with Stephan Baier, we prove a subconvexity
bound for Godement-Jacquet L-functions associated with Maass forms
for SL(3,Z). The bound arrives from extending a method of M. Jutila
(with new ingredients and innovations) on...
