Systems of many forms

27 October 2014
Simon Rydin Myerson

Consider a nonsingular projective variety $X$ defined by a system of $R$ forms of the same degree $d$. The circle method proves the Hasse principle and Manin's conjecture for $X$ when $\text{dim}X > C(d,R)$. I will describe how to improve the value of $C$ when $R$ is large. I use a technique for estimating mean values of exponential sums which I call a ``moat lemma". This leads to a novel and intriguing system of auxiliary inequalities.


  • Junior Number Theory Seminar