Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Marshall_Hall's_conjecture> ?p ?o. }
Showing items 1 to 27 of
27
with 100 items per page.
- Marshall_Hall's_conjecture abstract "In mathematics, Hall's conjecture is an open question, as of 2012, on the differences between perfect squares and perfect cubes. It asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie a substantial distance apart. This question arose from consideration of the Mordell equation in the theory of integer points on elliptic curves.The original version of Hall's conjecture, formulated by Marshall Hall, Jr. in 1970, says that there is a positive constant C such that for any integers x and y for which y2 ≠ x3,Hall suggested that perhaps C could be taken as 1/5, which was consistent with all the data known at the time the conjecture was proposed. Danilov showed in 1982 that the exponent 1/2 on the right side (that is, the use of |x|1/2) can't be replaced by any higher power: for no δ > 0 is there a constant C such that |y2 - x3| > C|x|1/2 + δ whenever y2 ≠ x3.In 1965, Davenport proved an analogue of the above conjecture in the case of polynomials: if f(t) and g(t) are nonzero polynomials over C such that g(t)3 ≠ f(t)2 in C[t], thenThe weak form of Hall's conjecture, due to Stark and Trotter around 1980, replaces the square root on the right side of the inequality by any exponent less than 1/2: for any ε > 0, there is some constant c(ε) depending on ε such that for any integers x and y for which y2 ≠ x3,The original, strong, form of the conjecture with exponent 1/2 has never been disproved, although it is no longer believed to be true and the term Hall's conjecture now generally means the version with the ε in it. For example, in 1998 Elkies found the example4478849284284020423079182 - 58538865167812233 = -1641843,for which compatibility with Hall's conjecture would require C to be less than .0214 ≈ 1/50, so roughly 10 times smaller than the original choice of 1/5 that Hall suggested.The weak form of Hall's conjecture would follow from the ABC conjecture. A generalization to other perfect powers is Pillai's conjecture.".
- Marshall_Hall's_conjecture wikiPageExternalLink hall.htm.
- Marshall_Hall's_conjecture wikiPageExternalLink hall.html.
- Marshall_Hall's_conjecture wikiPageID "7119900".
- Marshall_Hall's_conjecture wikiPageRevisionID "586646037".
- Marshall_Hall's_conjecture hasPhotoCollection Marshall_Hall's_conjecture.
- Marshall_Hall's_conjecture subject Category:Conjectures.
- Marshall_Hall's_conjecture subject Category:Number_theory.
- Marshall_Hall's_conjecture type Abstraction100002137.
- Marshall_Hall's_conjecture type Cognition100023271.
- Marshall_Hall's_conjecture type Concept105835747.
- Marshall_Hall's_conjecture type Conjectures.
- Marshall_Hall's_conjecture type Content105809192.
- Marshall_Hall's_conjecture type Hypothesis105888929.
- Marshall_Hall's_conjecture type Idea105833840.
- Marshall_Hall's_conjecture type PsychologicalFeature100023100.
- Marshall_Hall's_conjecture type Speculation105891783.
- Marshall_Hall's_conjecture comment "In mathematics, Hall's conjecture is an open question, as of 2012, on the differences between perfect squares and perfect cubes. It asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie a substantial distance apart. This question arose from consideration of the Mordell equation in the theory of integer points on elliptic curves.The original version of Hall's conjecture, formulated by Marshall Hall, Jr.".
- Marshall_Hall's_conjecture label "Congettura di Marshall Hall".
- Marshall_Hall's_conjecture label "Marshall Hall's conjecture".
- Marshall_Hall's_conjecture sameAs Congettura_di_Marshall_Hall.
- Marshall_Hall's_conjecture sameAs m.0h52w3.
- Marshall_Hall's_conjecture sameAs Q1165804.
- Marshall_Hall's_conjecture sameAs Q1165804.
- Marshall_Hall's_conjecture sameAs Marshall_Hall's_conjecture.
- Marshall_Hall's_conjecture wasDerivedFrom Marshall_Hall's_conjecture?oldid=586646037.
- Marshall_Hall's_conjecture isPrimaryTopicOf Marshall_Hall's_conjecture.