Gaussian almost primes in almost all narrow sectors



: Järviniemi, Olli; Teräväinen, Joni

Publisher: EUROPEAN MATHEMATICAL SOC-EMS

: BERLIN

: 2024

: Revista Matemática Iberoamericana

: REVISTA MATEMATICA IBEROAMERICANA

: REV MAT IBEROAM

: 40

: 4

: 1293

: 1350

: 58

: 0213-2230

DOI: https://doi.org/10.4171/RMI/1452

: https://ems.press/journals/rmi/articles/13272470

: https://research.utu.fi/converis/portal/detail/Publication/457146057


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.

Last updated on 2025-27-01 at 19:34