Threefield identities and simultaneous representations of primes by binary quadratic forms
Number Theory
2014-08-19 v1
Abstract
Kaplansky [2003] proved a theorem on the simultaneous representation of a prime by two different principal binary quadratic forms. Later, Brink found five more like theorems and claimed that there were no others. By putting Kaplansky-like theorems into the context of threefield identities after Andrews, Dyson, and Hickerson, we find that there are at least two similar results not on Brink's list. We also show how such theorems are related to results of Muskat on binary quadratic forms
Keywords
Cite
@article{arxiv.1208.1412,
title = {Threefield identities and simultaneous representations of primes by binary quadratic forms},
author = {Eric Mortenson},
journal= {arXiv preprint arXiv:1208.1412},
year = {2014}
}