Analytic methods for the distribution of rational points

Matching Funds - Steiermark

Disciplines

Mathematics (100%)

Keywords

Rational points, Arithmetic statistics, Analytic Number Theory, Diophantine equations

Abstract

Evidence of human civilisations searching for integer solutions to polynomial equations dates back over 3500 years, and it remains a problem of central importance in modern number theory. In this project, we are concerned with how likely it is that a ``randomly chosen" equation has a solution, and if it does have a solution, how many solutions are there? We aim to give precise quantitative answers to these questions, building new conjectures and expanding the scope of well established conjectures in the field by exploring examples at their limits.