An example in Beurling's theory of generalised primes

• Autorzy: Faez Al-Maamori , Titus Hilberdink
• Języki publikacji: EN

Abstrakty

EN

We prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes. The example has its generalised Chebyshev function given by [x]-1, and associated zeta function ζ₀(s) given via
$- (ζ'₀(s))/(ζ₀(s)) = ζ(s) - 1$,
where ζ is Riemann's zeta function. We study the behaviour of the corresponding Beurling integer counting function N(x), producing O- and Ω- results for the 'error' term. These are strongly influenced by the size of ζ(s) near the line Re s=1.

Kategorie tematyczne

• 11N80: Generalized primes and integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 4
• Strony: 383-395

Daty

wydano

2015

Twórcy

autor

Faez Al-Maamori

• Department of Mathematics, University of Babylon, Babylon, Iraq

autor

Titus Hilberdink

• Department of Mathematics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, UK

Identyfikatory

DOI

10.4064/aa168-4-4