Stephan Baier
Published 2017-06-20Version 1
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.
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
Fourier series and Diophantine approximation
Rational points near planar curves and Diophantine approximation
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