The large sieve with power moduli for ℤ[i]

2018/02/25 by Stephan Baier, Arpit Bansal, Baier, Stephan +1
Mathematics · #11L40 #11N35 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1802.08964

openalex publication_date 2018/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a large sieve inequality for power moduli in ℤ[i], extending earlier work by L. Zhao and the first-named author on the large sieve for power moduli for the classical case of moduli in ℤ. Our method starts with a version of the large sieve for ℝ². We convert the resulting counting problem back into one for ℤ[i] which we then attack using Weyl differencing and Poisson summation.

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