3 papers
math.CV2025
Bounded domains on Kobayashi hyperbolic manifolds covering compact complex manifolds
Nicholas Newsome
The lack of a uniformization theorem in several complex variables leads to a desire to classify all of the simply connected domains. We use established computational methods and a…
math.HO2017
A Proof of Symmetry of the Power Sum Polynomials using a Novel Bernoulli Numbers Identity
Nicholas J. Newsome, Maria S. Nogin, Adnan H. Sabuwala
The problem of finding formulas for sums of powers of natural numbers has been of interest to mathematicians for many centuries. Among these is Faulhaber's well-known formula expre…
math.NT2017
Congruences of Power Sums
Nicholas J. Newsome, Maria S. Nogin, Adnan H. Sabuwala
The following congruence for power sums, , is well known and has many applications: $1^n+2^n +\dots +p^n \equiv\begin{cases} -1 \text{ mod } p, & \text{ if } \ p-1 \ | \ n;…