Matches in SemOpenAlex for { <https://semopenalex.org/work/W4319941683> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W4319941683 endingPage "151" @default.
- W4319941683 startingPage "119" @default.
- W4319941683 abstract "Let $$alpha $$ be a real algebraic number of degree $$d ge 3$$ and let $$beta in {mathbb {Q}}(alpha )$$ be irrational. Let $$mu $$ be a real number such that $$(d/2) + 1< mu < d$$ and let $$C_0$$ be a positive real number. We prove that there exist positive real numbers $$C_1$$ and $$C_2$$ , which depend only on $$alpha $$ , $$beta $$ , $$mu $$ and $$C_0$$ , with the following property. If $$x_1/y_1$$ and $$x_2/y_2$$ are rational numbers in lowest terms such that $$begin{aligned} H(x_2, y_2) ge H(x_1, y_1) ge C_{1} end{aligned}$$ and $$begin{aligned} left| alpha - frac{x_1}{y_1}right|< frac{C_0}{H(x_1, y_1)^mu }, quad left| beta - frac{x_2}{y_2}right| < frac{C_0}{H(x_2, y_2)^mu }, end{aligned}$$ then either $$H(x_2, y_2) > C_{2}^{-1} H(x_1, y_1)^{mu - d/2}$$ , or there exist integers s, t, u, v, with $$sv - tu ne ~0$$ , such that $$begin{aligned} beta = frac{salpha + t}{ualpha + v} quad text {and} quad frac{x_2}{y_2} = frac{sx_1 + ty_1}{ux_1 + vy_1}, end{aligned}$$ or both. Here $$H(x, y) = max (|x|, |y|)$$ is the height of x/y. Since $$mu - d/2$$ exceeds 1, our result demonstrates that, unless $$alpha $$ and $$beta $$ are connected by means of a linear fractional transformation with integer coefficients, the heights of $$x_1/y_1$$ and $$x_2/y_2$$ have to be exponentially far apart from each other. An analogous result is established in the case when $$alpha $$ and $$beta $$ are p-adic algebraic numbers." @default.
- W4319941683 created "2023-02-11" @default.
- W4319941683 creator A5017460809 @default.
- W4319941683 date "2023-02-10" @default.
- W4319941683 modified "2023-09-23" @default.
- W4319941683 title "On the generalization of the gap principle" @default.
- W4319941683 cites W1512531712 @default.
- W4319941683 cites W1982324523 @default.
- W4319941683 cites W2002416196 @default.
- W4319941683 cites W2010380770 @default.
- W4319941683 cites W2030098631 @default.
- W4319941683 cites W2053669513 @default.
- W4319941683 cites W2078114900 @default.
- W4319941683 cites W2081291113 @default.
- W4319941683 cites W2591114074 @default.
- W4319941683 cites W283768719 @default.
- W4319941683 cites W4210736085 @default.
- W4319941683 cites W600381672 @default.
- W4319941683 doi "https://doi.org/10.1007/s10998-022-00505-2" @default.
- W4319941683 hasPublicationYear "2023" @default.
- W4319941683 type Work @default.
- W4319941683 citedByCount "0" @default.
- W4319941683 crossrefType "journal-article" @default.
- W4319941683 hasAuthorship W4319941683A5017460809 @default.
- W4319941683 hasBestOaLocation W43199416832 @default.
- W4319941683 hasConcept C114614502 @default.
- W4319941683 hasConcept C121332964 @default.
- W4319941683 hasConcept C185592680 @default.
- W4319941683 hasConcept C199360897 @default.
- W4319941683 hasConcept C24890656 @default.
- W4319941683 hasConcept C2775997480 @default.
- W4319941683 hasConcept C33923547 @default.
- W4319941683 hasConcept C41008148 @default.
- W4319941683 hasConcept C8010536 @default.
- W4319941683 hasConcept C94020503 @default.
- W4319941683 hasConcept C97137487 @default.
- W4319941683 hasConceptScore W4319941683C114614502 @default.
- W4319941683 hasConceptScore W4319941683C121332964 @default.
- W4319941683 hasConceptScore W4319941683C185592680 @default.
- W4319941683 hasConceptScore W4319941683C199360897 @default.
- W4319941683 hasConceptScore W4319941683C24890656 @default.
- W4319941683 hasConceptScore W4319941683C2775997480 @default.
- W4319941683 hasConceptScore W4319941683C33923547 @default.
- W4319941683 hasConceptScore W4319941683C41008148 @default.
- W4319941683 hasConceptScore W4319941683C8010536 @default.
- W4319941683 hasConceptScore W4319941683C94020503 @default.
- W4319941683 hasConceptScore W4319941683C97137487 @default.
- W4319941683 hasIssue "1" @default.
- W4319941683 hasLocation W43199416831 @default.
- W4319941683 hasLocation W43199416832 @default.
- W4319941683 hasOpenAccess W4319941683 @default.
- W4319941683 hasPrimaryLocation W43199416831 @default.
- W4319941683 hasRelatedWork W1516407058 @default.
- W4319941683 hasRelatedWork W1967784590 @default.
- W4319941683 hasRelatedWork W1978042415 @default.
- W4319941683 hasRelatedWork W1996842245 @default.
- W4319941683 hasRelatedWork W2041932452 @default.
- W4319941683 hasRelatedWork W2051491955 @default.
- W4319941683 hasRelatedWork W2319091001 @default.
- W4319941683 hasRelatedWork W2322893049 @default.
- W4319941683 hasRelatedWork W2949760713 @default.
- W4319941683 hasRelatedWork W4323666601 @default.
- W4319941683 hasVolume "87" @default.
- W4319941683 isParatext "false" @default.
- W4319941683 isRetracted "false" @default.
- W4319941683 workType "article" @default.