Special Year 2009-10: Analytic Number Theory

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...