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arXiv · 1307.0443

Metacommutation of Hurwitz primes

Henry Cohn·Abhinav Kumar
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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.

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Henry Cohn, Abhinav Kumar. 2013-07-01. Metacommutation of Hurwitz primes. https://doi.org/10.1090/s0002-9939-2014-12358-6

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