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Beurling generalized integers with the Delone Property
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Jeffrey C. Lagarias
Published/Copyright:
August 26, 2008
Abstract
A set 
of Beurling generalized integers consists of the unit n0 = 1 plus the set n1 ≤ n2 ≤ … of all power products of a set of generalized primes 1 < g1 ≤ g2 ≤ g3 ≤ … with gi → ∞, with these power products arranged in increasing order and counted with multiplicity. We say that has the Delone property if there are positive constants r, R such that R ≥ ni + 1 – ni ≥ r for all i ≥ 1. Any set with the Delone property has unique factorization into irreducible elements and is therefore a subsemigroup of ℝ+. We classify all such semigroups which are contained in the integers 
. The set of generalized primes of any such consists of all but finitely many primes, plus finitely many other composites.
Received: 1997-11
Published Online: 2008-08-26
Published in Print: 1999-May
© de Gruyter 1999
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Articles in the same Issue
- Simple automorphism groups of cycle-free partial orders
- Beurling generalized integers with the Delone Property
- Indefinite quadratic forms and Eisenstein series
- Lax embeddings of polar spaces in finite projective spaces
- Disjoint unions of complex affine subspaces interpolating for Ap
- Boundary compactifications of SL(2, ℝ) and SL(2, ℂ)
Articles in the same Issue
- Simple automorphism groups of cycle-free partial orders
- Beurling generalized integers with the Delone Property
- Indefinite quadratic forms and Eisenstein series
- Lax embeddings of polar spaces in finite projective spaces
- Disjoint unions of complex affine subspaces interpolating for Ap
- Boundary compactifications of SL(2, ℝ) and SL(2, ℂ)
