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arXiv · 1802.08964

The large sieve with power moduli for $\mathbb{Z}[i]$

Stephan Baier·Arpit Bansal
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Abstract

We establish a large sieve inequality for power moduli in $\mathbb{Z}[i]$, 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 $\mathbb{Z}$. Our method starts with a version of the large sieve for $\mathbb{R}^2$. We convert the resulting counting problem back into one for $\mathbb{Z}[i]$ which we then attack using Weyl differencing and Poisson summation.

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Stephan Baier, Arpit Bansal. 2018-02-25. The large sieve with power moduli for $\mathbb{Z}[i]$. https://arxiv.org/abs/1802.08964

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