Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...

Arithmetic circuit complexity investigates the computational resources required to evaluate polynomial functions via networks of arithmetic operations. At its core, this field seeks to classify ...

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 ...

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 ...