Gaussian almost primes in almost all narrow sectors

• Olli Järviniemi ^[1] ; Joni Teräväinen ^[1]
  1. [1] University of Turku

     University of Turku

     Turku, Finlandia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 4, 2024, págs. 1293-1350
• Idioma: inglés
• DOI: 10.4171/RMI/1452
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• Resumen

  • We show that almost all sectors of the disc {z∈C:∣z∣ 2≤X} of area (logX) 15.1 contain products of exactly two Gaussian primes, and that almost all sectors of area (logX) 1+ε 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.