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Reciprocal of the square root of a perfect power
| Content Provider | Semantic Scholar |
|---|---|
| Author | Jakimczuk, Rafael Gustavo |
| Copyright Year | 2016 |
| Abstract | Let us consider the sum ∑ P≤x 1 √ P where P denotes a perfect power. In a previous article we obtained the formula ∑ P≤x 1 √ P = 1 2 log x+ C + o(1) where C is a constant. In this article we obtain more precise asymptotic formulae. Besides we prove that C is positive and C = γ + ∑ P ′ 1 √ P ′ where γ > 0 is the Euler’s constant and P ′ denotes a perfect power not a square. Mathematics Subject Classification: 11A99, 11B99 |
| Starting Page | 21 |
| Ending Page | 26 |
| Page Count | 6 |
| File Format | PDF HTM / HTML |
| DOI | 10.12988/imf.2016.5867 |
| Alternate Webpage(s) | http://www.m-hikari.com/imf/imf-2016/1-4-2016/p/jakimczukIMF1-4-2016.pdf |
| Alternate Webpage(s) | https://doi.org/10.12988/imf.2016.5867 |
| Volume Number | 11 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |