European Journal of Mathematics

, Volume 3, Issue 3, pp 614–649 | Cite as

Diophantine approximation on lines in \(\mathbb {C}^2\) with Gaussian prime constraints

Research Article
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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 Gaussian primes 

Mathematics Subject Classification

11J83 11K60 11L07 
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Notes

Acknowledgements

The author would like to thank Prof. Anish Ghosh for useful discussions about this topic at and after a pleasant stay at the Tata Institute in Mumbai in August 2016. He would further like to thank the anonymous referee for useful comments on a first version of this paper which greatly helped to make this paper self-contained.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Physical SciencesJawaharlal Nehru University, MunirkaDelhiIndia

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