Add to ORKG78 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.Following A. Beurling (Acta Math. 68 (1937) 255-291), we consider a set of generalized prime numbers $P=\{1<p\sb1\le p\sb2\le\...\}$ and the set of generalized integers $N=\{n\sb1=1\le n\sb2\le\...\}$ generated by P. We let $N(x)$ be the counting function of the set N. In this thesis we give continuous versions of generalized number systems considered by R. S. Hall (Proc. Amer. Math. Soc. 40 (1973) 79-82). We provide an explicit calculation of the associated zeta function, which in turn allows us to obtain an expression for $N(x)$ with several terms rather than just an O-term for the error. We construct examples that illustrate a theorem of W.-B. Zhang (Illinois J. Math. ...
In 1997 H.G.Diamond gave a condition on Beurling’s generalized prime numbers in order that the corre...
AbstractAsymptotic behaviour of the counting function of Beurling integers is deduced from Chebyshev...
In this thesis we extend two important theorems in analytic prime number theory to a the setting of ...
78 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.Following A. Beurling (Acta Ma...
We study generalized prime systems P and generalized integer systems N obtained from them. The asymp...
144 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986.This paper is a study by &quo...
We show that Halász’s theorem holds for Beurling numbers under the following two mild hypotheses on ...
75 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1967.U of I OnlyRestricted to the U...
AbstractLet P = {pj}j=1∞, where 1 < p1 ≤ p2 ≤ …, pj → ∞. Following Beurling [Acta Math, 1937], we ca...
AbstractLet π(x) and N(x) be the respective counting functions of a set of generalized primes and a ...
Several examples of generalized number systems are constructed to compare various conditions occurri...
We show that for Beurling generalized numbers the prime number theorem in remainder form $$\pi(x) = ...
AbstractWe provide new sufficient conditions for Chebyshev estimates for Beurling generalized primes...
In classical prime number theory there are several asymptotic formulas said to be “equivalent” to th...
We study generalised prime (g-prime) systems $\calP$ and g-integer systems $\mathcal{N}$ obtained fr...
In 1997 H.G.Diamond gave a condition on Beurling’s generalized prime numbers in order that the corre...
AbstractAsymptotic behaviour of the counting function of Beurling integers is deduced from Chebyshev...
In this thesis we extend two important theorems in analytic prime number theory to a the setting of ...
78 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.Following A. Beurling (Acta Ma...
We study generalized prime systems P and generalized integer systems N obtained from them. The asymp...
144 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986.This paper is a study by &quo...
We show that Halász’s theorem holds for Beurling numbers under the following two mild hypotheses on ...
75 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1967.U of I OnlyRestricted to the U...
AbstractLet P = {pj}j=1∞, where 1 < p1 ≤ p2 ≤ …, pj → ∞. Following Beurling [Acta Math, 1937], we ca...
AbstractLet π(x) and N(x) be the respective counting functions of a set of generalized primes and a ...
Several examples of generalized number systems are constructed to compare various conditions occurri...
We show that for Beurling generalized numbers the prime number theorem in remainder form $$\pi(x) = ...
AbstractWe provide new sufficient conditions for Chebyshev estimates for Beurling generalized primes...
In classical prime number theory there are several asymptotic formulas said to be “equivalent” to th...
We study generalised prime (g-prime) systems $\calP$ and g-integer systems $\mathcal{N}$ obtained fr...
In 1997 H.G.Diamond gave a condition on Beurling’s generalized prime numbers in order that the corre...
AbstractAsymptotic behaviour of the counting function of Beurling integers is deduced from Chebyshev...
In this thesis we extend two important theorems in analytic prime number theory to a the setting of ...