Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...

In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, ...

All products featured on WIRED are independently selected by our editors. However, we may receive compensation from retailers and/or from purchases of products through these links. Learn more. Adding ...

Joseph Silverman is a world-leading mathematician working in the general area of Number Theory, and more specifically in Diophantine and arithmetic geometry, elliptic curves and cryptography. Joseph ...