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A LOWER-BOUND FOR A WEIGHTED PRODUCT OF THE CONJUGATES OF A TOTALLY-REAL ALGEBRAIC INTEGER
Journal article

A LOWER-BOUND FOR A WEIGHTED PRODUCT OF THE CONJUGATES OF A TOTALLY-REAL ALGEBRAIC INTEGER

T Zaimi
Comptes rendus de l'Académie des sciences. Série I. Mathématique, Vol.318(1), pp.1-4
06/01/1994

Abstract

Mathematics Physical Sciences Science & Technology
If x denotes a totally real algebraic integer with minimal polynomial P over Q of degree n and with conjugates x(I), x(2),..., x(n) satisfying \x(1)\ greater than or equal to \x(2)\ greater than or equal to ... greater than or equal to \x(n)\, we give a lower bound of the quantity \x(1)(n-1) x(2)(R-2) ... x(n-1)\ depending on the degree n and on the discriminant of P.

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