On the set of divisors of Gaussian integers
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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.
KeywordsGaussian integers Divisor function Erdős conjecture on divisor function
Mathematics Subject ClassificationPrimary 11N25 11N36 Secondary 11L03
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.