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001-es BibID:	BIBFORM111874
Első szerző:	Győry Kálmán (matematikus)
Cím:	Résultats effectifs sur la représentation des entiers par des formes décomposables / Kálmán Györy
Dátum:	1980
Megjelenés:	Kingston : Queen's University, 1980
Terjedelem:	142 p.
Megjegyzések:	(Queen's Papers in Pure and Applied Mathematics, 0079-8797 ; 56.) A form F(x1,?,xn) is said to be decomposable if it is a product of linear factors, and these factors may be described as "connected'' if each factor belongs to a triple of factors linearly dependent over the field of constants. Consider now a Diophantine equation, in integers x1,?,xn of k, F(x1,?,xn)=m over an algebraic number field k, where m need only be supposed fixed up to factors belonging to some finite set S of prime ideals, and where F is decomposable connected. Each connection relation yields a relation 1+?2+?3=0 with ?i of the shape ?=??1?1?2b2??rbr. Here each ? has only finitely many possibilities in K, some extension of k depending on F, the ?j are S-units of K and the bj are rational integers. Lower bounds for linear forms in the logarithms of algebraic numbers (the so-called Baker inequalities in the complex and p-adic cases) suffice to show that the \|bj\| are bounded by an effectively computable constant and, up to trivial common factors, this allows one to determine all possibilities for the linear factors of F. A further condition on the linear factors, say "strong connectedness'', may then allow one to determine effectively all possibilities for the unknown xi. For example, n=2 and F at least 3 distinct factors always yields strong connectedness. ...
Tárgyszavak:	Természettudományok Matematika- és számítástudományok monográfia könyv decomposable forms algebraic fields
További szerzők:	Queen's Papers in Pure and Applied Mathematics
Internet cím:	Intézményi repozitóriumban (DEA) tárolt változat
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