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On the set of divisors of Gaussian integers

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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.

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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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  1. Saurabh Kumar Singh

    Present address: Institute for Number Theory and Probability Theory, University of Ulm, 89069, Ulm, Germany

Authors and Affiliations

  1. Institute for Number Theory and Probability Theory, University of Ulm, 89069, Ulm, Germany

    Helmut Maier

  2. Stat-Math Unit, Indian Statistical Institute, 203 BT Road, Kolkata, 700108, India

    Saurabh Kumar Singh

Authors
  1. Helmut Maier
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  2. Saurabh Kumar Singh
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Correspondence to Saurabh Kumar Singh.

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The research of the second author was partially supported by the Department of Atomic Energy, Government of India, NBHM post doctoral fellowship no: 2/40(15)/2016/R&D-II/5765.

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Maier, H., Singh, S.K. On the set of divisors of Gaussian integers. Ramanujan J 50, 355–366 (2019). https://doi.org/10.1007/s11139-019-00158-9

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  • DOI: https://doi.org/10.1007/s11139-019-00158-9

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