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 ...

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with number ...

Mathematical methods and special functions have long served as the backbone of modern theoretical physics and applied mathematics. These tools enable researchers to solve complex differential ...

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 ...

I am a Ph.D. graduate of Emory University (2018), having worked under the supervision of Ken Ono. My research interests lie primarily in number theory and combinatorics, in particular the theory of ...

A rule for creating a "y" output from an "x" input. For example, the y value of the function f(x) = 15x is 30 if x is 2. THIS DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction requires ...

The Handbook of Mathematical Functions by Milton Abramovich and Irene Stegun is the one book I would wish to have on a desert island. Unlike a novel, it withstands infinities of rereadings. Its ...