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The Ramanujan Journal

, Volume 50, Issue 2, pp 355–366 | Cite as

On the set of divisors of Gaussian integers

  • Helmut Maier
  • Saurabh Kumar SinghEmail author
Article
  • 94 Downloads

Abstract

In Maier and Tenenbaum (Invent Math 76(1):121–128, 1984), Tenenbaum and the first author proved an old conjecture of Paul Erdős about the propinquity of divisors of integers. In this paper, we prove an analogous results for Gaussian integers.

Keywords

Gaussian integers Divisor function Erdős conjecture on divisor function 

Mathematics Subject Classification

Primary 11N25 11N36 Secondary 11L03 

Notes

Acknowledgements

The Saurabh Kumar Singh is thankful to the Institute of Number Theory and Probability Theory, University of Ulm, Germany for its warm hospitality and generous support.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Number Theory and Probability TheoryUniversity of UlmUlmGermany
  2. 2.Institute for Number Theory and Probability TheoryUniversity of UlmUlmGermany
  3. 3.Stat-Math UnitIndian Statistical InstituteKolkataIndia

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