This is an exposition of work on Artin's Conjecture on the zeros
of p-adic forms.A variety of lines of attack are described ,going
back to 1945.However there is particular emphasis on recent
developments concerning quartic forms on the one hand ,and...
The Ramanujan conjecture states that for a holomorphic cusp form
$f(z) =\sum_{n \in N} \lambda_f(n)e(nz)$ of weight $k$, the
coefficients $\lambda_f(n)$ satisfy the bound $|\lambda_f(n)|
\ll_\epsilon n^{(k−1)/2+\epsilon}$. In the case where $k$ is...
This is an exposition of work on Artin's Conjecture on the zeros
of p-adic forms.A variety of lines of attack are described ,going
back to 1945.However there is particular emphasis on recent
developments concerning quartic forms on the one hand ,and...
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...
