Diophantine definition
Examples of Diophantine in a sentence
Elliptic curves (smooth curves of genus 1 that have a K rational point) have formed a paradigm on the way to look for results in Diophantine equations.
Number theory, and especially the study of Diophantine equations, can be considered a core mathematical study.
Specifically, the work of ▇▇▇▇ and ▇▇▇▇▇▇▇-▇▇▇▇▇ [2] in 2012 utilized these ideas of rank functions, but applied them in an algebro-geometric context to study Diophantine problems, allowing them to combinatorially bound numbers of solutions to equations.
In this regard, we also need the solution to a classical Diophantine problem.
Diophantine geometry: an introduction, volume 201 of Graduate Texts in Math- ematics.
We recall that a Diophantine equation is a system of polynomial equa- tions over a field K, and therefore it can be thought of as a subset of the affine space Kn. This simple idea gave number theorists a whole new arsenal of techniques to tackle old problems.
We use our results to give algorithmic, geometric and Diophantine applications in the following two chapters.
The idea is to show that every cross-ratio satisfies a well-studied Diophantine equation.
This interplay between number theory and algebraic geometry can be used to find a natural, though unexpected, way to categorise Diophantine equa- tions; the dimension of the zero locus.
The authors want to thank ▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇ for his comments that improved the exposition and ▇▇▇▇ ▇▇▇▇▇▇▇▇▇▇▇ for his help on the Diophantine approximation part.