A1 Refereed original research article in a scientific journal
Gaussian almost primes in almost all narrow sectors
Authors: Järviniemi, Olli; Teräväinen, Joni
Publisher: EUROPEAN MATHEMATICAL SOC-EMS
Publishing place: BERLIN
Publication year: 2024
Journal: Revista Matemática Iberoamericana
Journal name in source: REVISTA MATEMATICA IBEROAMERICANA
Journal acronym: REV MAT IBEROAM
Volume: 40
Issue: 4
First page : 1293
Last page: 1350
Number of pages: 58
ISSN: 0213-2230
DOI: https://doi.org/10.4171/RMI/1452
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://ems.press/journals/rmi/articles/13272470
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457146057
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
We show that almost all sectors of the disc {z is an element of C : vertical bar z vertical bar(2) <= X} of area (log X)(15.1) contain products of exactly two Gaussian primes, and that almost all sectors of area (log X)(1+epsilon) contain products of exactly three Gaussian primes. The argument is based on mean value theorems, large value estimates and pointwise bounds for Hecke character sums.
Keywords:
Almost primes, Dirichlet polynomials, Gaussian integers, narrow sectors
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