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Harmonic sets and the harmonic prime number theorem
Published online by Cambridge University Press: 17 April 2009
Extract
We restrict primes and prime powers to sets . Let . Then the error in θH(x) has, unconditionally, the expected order of magnitude . However, if then ψH (x) = x log 2 + O (log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem”, πH (x)/π (x) → log 2.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 127 - 137
- Copyright
- Copyright © Australian Mathematical Society 2005