Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version

Stephan Baier

Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version

Number Theory 2017-06-21 v1

Authors: Stephan Baier

Abstract

We study the problem of Diophantine approximation on lines in $\mathbb{C}^2$ with numerators and denominators restricted to Gaussian primes. To this end, we develop analogs of well-known results on small fractional parts of $p\gamma$ , $p$ running over the primes and $\gamma$ being a fixed irrational, for Gaussian primes.

Keywords

diophantine approximation diophantine equations gaussian random fields

Cite

@article{arxiv.1706.06453,
  title  = {Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version},
  author = {Stephan Baier},
  journal= {arXiv preprint arXiv:1706.06453},
  year   = {2017}
}

Comments

32 pages. This is a combination of slightly extended versions of my papers arXiv:1609.08745 and arXiv:1612.02622, with the goal to make arXiv:1612.02622 completely self-contained

Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version

Abstract

Keywords

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