The large sieve with square norm moduli in ℤ[i]
Stephan Baier1
1 School of Physical Sciences Jawarhal Nehru University Delhi Delhi 110067, India
Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 1, pp. 93-115.

We prove a large sieve inequality for square norm moduli in ℤ[i].

Nous montrons une inégalité de grand cible pour les normes dans ℤ[i].

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.1018
Classification: 11L03, 11R04
Keywords: Large Sieve, Gaussian integers
Stephan Baier 1

1 School of Physical Sciences Jawarhal Nehru University Delhi Delhi 110067, India
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Stephan Baier. The large sieve with square norm moduli in $\protect \mathbb{Z}[i]$. Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 1, pp. 93-115. doi : 10.5802/jtnb.1018. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1018/

[1] Stephan Baier On the large sieve with sparse sets of moduli, J. Ramanujan Math. Soc., Volume 21 (2006) no. 3, pp. 279-295 | MR | Zbl

[2] Stephan Baier; Liangyi Zhao An improvement for the large sieve for square moduli, J. Number Theory, Volume 128 (2008) no. 1, pp. 154-174 | DOI | MR | Zbl

[3] Enrico Bombieri; Henryk Iwaniec On the order of ζ(1/2+it), Ann. Sc. Norm. Super. Pisa, Cl. Sci., Volume 13 (1986), pp. 449-472

[4] Martin N. Huxley The large sieve inequality for algebraic number fields, Mathematika, Lond., Volume 15 (1968), pp. 178-187 | DOI | MR | Zbl

[5] Waldemar Schlackow A sieve problem over the Gaussian integers, University of Oxford, UK (2010) (Ph. D. Thesis)

[6] Liangyi Zhao Large sieve inequality for characters to square moduli, Acta Arith, Volume 112 (2004), pp. 297-308 | DOI | MR | Zbl

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