An omega-result for Beurling generalized integers
Tom 212 / 2024
Acta Arithmetica 212 (2024), 359-371
MSC: Primary 11N80; Secondary 11M41
DOI: 10.4064/aa230324-20-11
Opublikowany online: 21 February 2024
Streszczenie
We consider Beurling number systems with very well-behaved primes, in the sense that for some \alpha \lt 1/2. We investigate how small the error term in the asymptotic formula for the integer-counting function N(x) can be for such systems. In particular, we show that N(x) - \rho x = \Omega (\sqrt{x}\,\mathrm e^{-(\log x)^{\beta }}) for any \beta \gt 2/3.
