An asymptotic formula for elements of a semigroup of integers
An example in Beurling's theory of generalised primes
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 , 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...
An example in Beurling's theory of primes
Analytic and arithmetic theory of semigroups with divisor theory
Analytic number theory in formations based on additive arithmetical semigroups.
Arithmetical properties of finite rings and algebras, and analytical number theory. V. Categories and relative analytic number theory.
Arithmetical semigroups I: direct factors.
Arithmetical semigroups II: sieving by large and small prime elements. Sets of multiples.
Arithmetical Semigroups III: Elements With Prime Factors in Residue Classes.
Arithmetical Semigroups V: Multiplicative Functions.
Asymptotic density in combined number systems.