Metacommutation of Hurwitz primes

Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes

We formulate Goldbach type questions for Gaussian, Hurwitz, Octavian and Eisenstein primes.

The power digraphs of safe primes

A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of th...

Hurwitz’ Theorem

In this article we describe several results based on the paper [Hur98] and which we will refer to as Hurwitz’ theorem. There are several related results: the classification of real normed division algebras, the classification of complex composition algebras and the classification of real composition algebras. The classification of real division algebras is an open problem. Our interest is in co...

Hurwitz spaces

1.1 The classical Hurwitz space and the moduli of curves The classical Hurwitz space first appeared in the work of Clebsch [5] and Hurwitz [17] as an auxiliary object to study the moduli space of curves. Let X be a smooth projective curve of genus g over C. A rational function f : X → P of degree n is called simple if there are at least n − 1 points on X over every point of P. Such a cover has ...

Lemmata zum Hurwitz-Kriterium