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.


Almost primes, Dirichlet polynomials, Gaussian integers, narrow sectors

Last updated on 27/01/2025 07:34:41 PM