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.
Research Output
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1
Citations
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3
Publications