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Large sieve with sparse sets of moduli for $\mathbb{Z}[i]$

Volume 196 / 2020

Stephan Baier, Arpit Bansal Acta Arithmetica 196 (2020), 17-34 MSC: 11L40, 11N35. DOI: 10.4064/aa190329-10-3 Published online: 9 July 2020


We establish a general large sieve inequality with sparse sets $\mathcal {S}$ of moduli in the Gaussian integers which are in a sense well-distributed in arithmetic progressions. This extends earlier work of S. Baier on the large sieve with sparse sets of moduli. We then use this result to obtain large sieve bounds for the cases when $\mathcal {S}$ consists of squares of Gaussian integers and of Gaussian primes. Our bound for the case of square moduli improves our recent result [Int. J. Number Theory 14 (2018)].


  • Stephan BaierDepartment of Mathematics
    Ramakrishna Mission Vivekananda
    Educational and Research Institute
    G. T. Road, PO Belur Math
    Howrah, West Bengal 711202, India
  • Arpit BansalSchool of Physical Sciences
    Jawaharlal Nehru University
    New Delhi 110067, India

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