Harmonic sets and the harmonic prime number theorem
| dc.contributor.author | Broughan, Kevin A. | |
| dc.contributor.author | Casey, Rory J. | |
| dc.date.accessioned | 2009-02-22T21:02:28Z | |
| dc.date.available | 2009-02-22T21:02:28Z | |
| dc.date.issued | 2005 | |
| dc.description.abstract | We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2. | en |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | Broughan, K.A. & Casey, R. J. (2005). Harmonic sets and the harmonic prime number theorem. Bulletin of the Australian Mathematical Society, 71, 127-137. | en |
| dc.identifier.doi | 10.1017/S0004972700038089 | en_NZ |
| dc.identifier.uri | https://hdl.handle.net/10289/2038 | |
| dc.language.iso | en | |
| dc.publisher | Australian Mathematical Publishing Association Inc. | en_NZ |
| dc.relation.isPartOf | Bulletin of the Australian Mathematical Society | en_NZ |
| dc.relation.uri | http://www.austms.org.au/Bulletin | en |
| dc.rights | This article has been published in the journal: Bulletin of the Australian Mathematical Society. ©2005 Australian Mathematical Society. Used with Permission. | en |
| dc.subject | harmonic prime number theorem | en |
| dc.title | Harmonic sets and the harmonic prime number theorem | en |
| dc.type | Journal Article | en |
| dspace.entity.type | Publication | |
| pubs.begin-page | 127 | en_NZ |
| pubs.end-page | 137 | en_NZ |
| pubs.issue | 1 | en_NZ |
| pubs.volume | 71 | en_NZ |