Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

Let (X, μ) be a probability measure space and $T_{1},\ldots ,T_{n}$ be a family of commuting, measure preserving invertible transformations on X. Let $Q(m_{1},\ldots ...

A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine ...

Arithmetic geometry and Diophantine geometry lie at the confluence of number theory and algebraic geometry, exploring the deep connections between the arithmetic properties of numbers and the ...