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An example in Beurling's theory of generalised primes

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Al-Maamori F., Hilberdink T.

Acta Arithmetica

2015

tom 168

nr 4

383-395

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.

Ograniczanie wyników

1 Acta Arithmetica

1 Al-Maamori F.

1 Hilberdink T.

1 2015

Wyniki wyszukiwania

An example in Beurling's theory of generalised primes