A set of puzzles called Diophantine problems are often simple to state but hard to solve—though progress could have big implications for the future of mathematics Diophantine geometry is the field of ...

Diophantine equations stand at the interface of algebra, geometry and arithmetic, seeking integer or rational solutions to polynomial equations. Classical problems such as Pythagorean triples and ...

In this paper, we construct holomorphic families of Riemann surfaces from Veech groups and characterize their holomorphic sections by some points of corresponding flat surfaces. The construction gives ...