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Johann Christian Stumpenhusen

Publications and source records attributed to Johann Christian Stumpenhusen.

4 recordsLinked to original sources
arXiv2024

On the Proportion of Coprime Fractions in Number Fields

In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fraction as soon as it ``appears'' for the first time and no later. The natural density of coprime fractions in the set of reduced fractions may then be computed using well-known facts about Hecke $L$-functions. Furthermore, we draw some connections to the modular group and Heegner points.

math.NT↗
arXiv2024

On the Gaussian Moat Problem

The Gaussian Moat Problem asks whether it is possible to walk from the origin to infinity in the complex plane using only Gaussian primes as stepstones and steps of bounded length. We prove that this is not possible.

math.NT↗
arXiv2022

Perfect Eisenstein integers

We generalise the sum-of-divisors-function $σ$ and evenness to the rings of integers of certain algebraic number fields. In particular, we present necessary and sufficient conditions for even Eisenstein integers to be (norm-)perfect based on the work of McDaniel [McD] on Gaussian integers. Furthermore, some results concerning odd norm-perfect Eisenstein integers and the rings of integers of other cyclotomic fields are proven.

math.NT↗