An irrationality measure for Liouville numbers and conditional measures for Euler's constant
| dc.creator | Sondow, Jonathan | |
| dc.date | 2003-07-23 | |
| dc.date.accessioned | 2026-07-07T04:59:51Z | |
| dc.date.available | 2026-07-07T04:59:51Z | |
| dc.description | The irrationality exponent $μ(t)$ of an irrational number t, defined using the irrationality measure $1/q^μ$, distinguishes among non-Liouville numbers and is infinite for Liouville numbers. Using the irrationality measure $1/β^q$, we define the "irrationality base" $β(t)$, which distinguishes among Liouville numbers and is 1 for non-Liouville numbers. We give some properties and examples. Assuming a condition on certain linear forms in logarithms, for which we present numerical evidence supplied by P. Sebah, we prove an upper bound on the irrationality base of Euler's constant, $γ$. If $γ$ is irrational and the condition turns out to be false in a certain strong sense, we prove an upper bound on $μ(γ)$. | |
| dc.description | 12 pages, 1 figure, details of part of a talk at Journeés Arithmetiques XXIII in Graz | |
| dc.identifier | https://arxiv.org/abs/math/0307308 | |
| dc.identifier | http://arxiv.org/abs/math/0307308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68154 | |
| dc.subject | Number Theory | |
| dc.subject | 11J82 (Primary), 11J86 (Secondary) | |
| dc.title | An irrationality measure for Liouville numbers and conditional measures for Euler's constant | |
| dc.type | text |