Very elementary interpretations of the Euler-Mascheroni constant from counting divisors in intervals
| dc.creator | Feldman, David V. | |
| dc.date | 2008-10-08 | |
| dc.date.accessioned | 2026-07-07T10:08:28Z | |
| dc.date.available | 2026-07-07T10:08:28Z | |
| dc.description | Theorem 1 Let F:N-->R stand for any function which a) $F$ monotonically weakly increases; b) $F$ tends to infinity; and c) such that $q/F(q)$ tends to infinity. Let Z_F(q) equal the number of divisors of q less than sqrt{F(q)} minus the number of divisors of q between sqrt{F(q)} and F(q). Then, on the average, Z_F(q) equals Euler's constant Theorem 2 Fix a in (0,1). Write A for the average number of divisors of n that lie in (0,sqrt{a n}) minus the number of that lie in (sqrt{a n},a n)$. Then A= (sum_{i=1}^{\lceil {1-a}/a \rceil} \frac{1}{i}) - ln(1/a). | |
| dc.description | 14 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0810.1354 | |
| dc.identifier | http://arxiv.org/abs/0810.1354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171004 | |
| dc.subject | Number Theory | |
| dc.subject | 11Y60,11N25 | |
| dc.title | Very elementary interpretations of the Euler-Mascheroni constant from counting divisors in intervals | |
| dc.type | text |