H. Graves

activity

20092026

most citedEuclidean Ideals in Quadratic Imaginary Fields

2 citations · 3 across the 11 of their papers we have counts for

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3 papers · 1 filter

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…

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