H. Graves

collaborators

4 papers

math.NT2026

Sizes of Pre-Images of the Minimal Euclidean Function on the Gaussian Integers

Hester Graves

In 2023, the author presented the first computable minimal Euclidean function for a non-trivial number field. Along with a formula for $I ¨ _{Z [i]}$ , the minimal Euclidean f…

math.NT2025

The abc conjecture implies infinitely many non-Wieferich places for fixed bases in number fields

Hester Graves, Benjamin Weiss

Silverman showed that, assuming the $ab c$ conjecture, there are $≫ lo g x$ non-Wieferich primes base $a$ less than $x$ \cite{silverman}, for all non-zero $a$ . This inspired Grave…

math.NT2025

A Division Algorithm for the Gaussian Integers' Minimal Euclidean Function

Hester Graves

The usual division algorithms on $Z$ and $Z [i]$ measure the size of remainders using the norm function. These rings are Euclidean with respect to several function…

math.NT2025

Primes of the Form $m^{2} + 1$ and Goldbach's `Other Other' Conjecture

Jon Grantham, Hester Graves

We compute all primes up to $6.25 \times 1 0^{28}$ of the form $m^{2} + 1$ . Calculations using this list verify, up to our bound, a less famous conjecture of Goldbach. We introduce `Gold…

Sizes of Pre-Images of the Minimal Euclidean Function on the Gaussian Integers

The abc conjecture implies infinitely many non-Wieferich places for fixed bases in number fields

A Division Algorithm for the Gaussian Integers' Minimal Euclidean Function

Primes of the Form m2+1 and Goldbach's `Other Other' Conjecture

Primes of the Form $m^{2} + 1$ and Goldbach's `Other Other' Conjecture