Well-behaved Beurling primes and integers

✍ Scribed by Titus W. Hilberdink

• Book ID: 104024513
• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 221 KB
• Volume: 112
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.09.001

✦ Synopsis

In this paper, we study generalised prime systems for which both the prime and integer counting functions are asymptotically well-behaved, in the sense that they are approximately li(x) and x, respectively (where is a positive constant), with error terms of order O(x 1 ) and O(x 2 ) for some 1 , 2 < 1. We show that it is impossible to have both 1 and 2 less than 1 2 .