Some examples related to the \(abc\)-conjecture for algebraic number fields. (English) Zbl 0971.11009
The author constructs a numerical method for obtaining identities related to the uniform \(abc\)-conjecture for algebraic number fields.
Reviewer: Richard A. Mollin (Calgary)
MSC:
11D04 | Linear Diophantine equations |
11A55 | Continued fractions |
11Y65 | Continued fraction calculations (number-theoretic aspects) |
Keywords:
norm Euclidean; quadratic field; continued fraction; identities; uniform \(abc\)-conjectureReferences:
[1] | J. Browkin, The \(abc\)-conjecture, Preprint. · Zbl 0971.11010 |
[2] | J. Browkin and J. Brzeziński, Some remarks on the \?\?\?-conjecture, Math. Comp. 62 (1994), no. 206, 931 – 939. · Zbl 0804.11006 |
[3] | G. Cooke, A weakening of the euclidean property for integral domains and applications to algebraic number theory I, J. Reine Angew. Math. 282 (1976), 133-156. · Zbl 0328.13013 |
[4] | A. Granville and H.M. Stark, Abc implies no “Siegel zeros”, Preprint. · Zbl 0967.11033 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.