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001-es BibID:	BIBFORM111873
Első szerző:	Győry Kálmán (matematikus)
Cím:	On discriminant form and index form equations / K. Győry, Z. Z. Papp
Dátum:	1977
ISSN:	0081-6906
Megjegyzések:	Applying relatively recent refined inequalities for linear forms in the logarithms of algebraic numbers, the authors provide explicit bounds for the solutions of a certain class of Diophantine equations over algebraic number fields. Let K?L be algebraic number fields and let 1,?1,?,?m be linearly independent elements of K over L so that K=L(?1,?,?m). For an expression f defined over K, denote by DK/L(f) the difference product (discriminant) ?i?j(?if??jf) taken over all distinct pairs ?i,?j of embeddings of K in C over L. Then DK/L(?1x1+?+?mxm)=D is a form of degree k(k?1) with coefficients in L (where [L:K]=k). When k?3 the authors effectively determine all integers xi of L (up to unit multiples) satisfying the above equation in terms of the prime ideal factors of D (and of course the fields K,L). Equivalently the determination may be said to be of all elements xi with denominator divisible by only a nominated finite set of prime ideals, in terms of the height of D. Extensive reference is provided to the related literature. An immediate application of the cited result is to the matter of numbers represented by index forms F defined (in the case m=k?1) via DK/L(?1x1+?+?mxm)=F(x1,?,xm)DO, when 1,?1,?,?k?1 is the basis of an order O over L and DO its relative discriminant. The present paper is a p-adic generalisation of earlier results of the first author.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény hazai lapban folyóiratcikk
Megjelenés:	Studia Scientiarum Mathematicarum Hungarica. - 12 : 1-2 (1977), p. 47-60. -
További szerzők:	Papp Z. Z.
Internet cím:	Intézményi repozitóriumban (DEA) tárolt változat Szerző által megadott URL
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