We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A new generalized prime random approximation procedure and some of its applications.
- Authors
Broucke, Frederik; Vindas, Jasson
- Abstract
We present a new random approximation method that yields the existence of a discrete Beurling prime system P = { p 1 , p 2 , ⋯ } which is very close in a certain precise sense to a given non-decreasing, right-continuous, nonnegative, and unbounded function F. This discretization procedure improves an earlier discrete random approximation method due to Diamond et al. (Math Ann 334:1–36, 2006), and refined by Zhang (Math Ann 337:671–704, 2007). We obtain several applications. Our new method is applied to a question posed by Balazard concerning Dirichlet series with a unique zero in their half plane of convergence, to construct examples of very well-behaved generalized number systems that solve a recent open question raised by Hilberdink and Neamah (Int J Number Theory 16(05):1005–1011, 2020), and to improve the main result from (Adv Math 370:Article 107240, 2020), where a Beurling prime system with regular primes but extremely irregular integers was constructed.
- Subjects
NUMBER theory; RIEMANN hypothesis; OPEN-ended questions; DIRICHLET series
- Publication
Mathematische Zeitschrift, 2024, Vol 307, Issue 4, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-024-03526-4