A generalization of the prime number theorem
Abstract:A general theorem is introduced and proved, a special case of which is the prime number theorem (PNT). The main theorem proved in this article is the following: [image omitted], where F: → is analytic for all x ≥ 2, and the p's in the sum represent all primes p ≤ N. Since PNT is used to derive our generalization, we may say that PNT and our generalization are equivalent.
Document Type: Research Article
Publication date: July 1, 2008