Research Explorer

Project

Extremal problems in Fourier analysis and abstract analytic number theory.
Code
bof/baf/4y/2024/01/155
Duration
01 January 2024 → 31 December 2025
Funding
Regional and community funding: Special Research Fund
Research disciplines
  • Natural sciences
    • Number theory
    • Approximations and expansions
    • Functional analysis
    • Harmonic analysis on Euclidean spaces
    • Integral transforms, operational calculus
Keywords
extremal problems for the Fourier transform Beurling generalized prime numbers abstract analytic number theory
 
Project description

This project pursues new advances in abstract analytic number theory related to the asymptotic distribution of generalized primes and integers. Our chief aim is to settle a number of conjectures and open problems in the area concerning optimality of error terms by analyzing and also constructing Beurling zeta functions. We also investigate a family of extremal problems in Fourier analysis and apply our results to obtain novel complex Tauberian theorems.