Metacommutation of Hurwitz primes
Number Theory
2017-01-13 v2
Abstract
Conway and Smith introduced the operation of metacommutation for pairs of primes in the ring of Hurwitz integers in the quaternions. We study the permutation induced on the primes of norm p by a prime of norm q under metacommutation, where p and q are distinct rational primes. In particular, we show that the sign of this permutation is the quadratic character of q modulo p.
Keywords
Cite
@article{arxiv.1307.0443,
title = {Metacommutation of Hurwitz primes},
author = {Henry Cohn and Abhinav Kumar},
journal= {arXiv preprint arXiv:1307.0443},
year = {2017}
}
Comments
11 pages