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 ...

A polynomial is a chain of algebraic terms with various values of powers. There are some words and phrases to look out for when you're dealing with polynomials: \(6{x^5} - 3{x^2} + 7\) is a polynomial ...

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 ...

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The classical Multiply and Accumulate (MAC) architecture represents the best solution for the implementation of many general purpose algorithms. This structure is found in DSPs, and also in some ...

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 ...