caa a22 4500 386307466 CHVBK 20180307111534.0 cr unu---uuuuu 161130e198806 xx s 000 0 eng 10.1017/S1446788700032122 doi S1446788700032122 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032122 Formulas for some diophantine approximation constants [Elektronische Daten] Let M be a full Z-module in F a real number field of degree at least 3 with N(α) denoting the norm of α F. Given any nonzero number φ in M we make the plausible conjecture that one can find a number ß in M such that N(ß) = N(φ) and the algebraic conjugates of ß (not including ß) have ratios arbitraily near any given numbers consistent with the complex algebraic conjugates of elements of F. We use the conjecture to give explicit formulas for some diophantine approximation constants. Without the conjecture our methods lead to corresponding lower bounds for these constants. Copyright © Australian Mathematical Society 1988 10 F 10 nationallicence 10 F 25 nationallicence Cusick T. W. Department of Mathematics State University of New York Buffalo, New York 14214, U.S.A. Krass S. School of Mathematics University of New South Wales Kensington, New South Wales 2033, Australia Journal of the Australian Mathematical Society Cambridge University Press 44/3(1988-06), 311-323 1446-7887 44:3<311 1988 44 JAZ https://doi.org/10.1017/S1446788700032122 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032122 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cusick T. W. Department of Mathematics State University of New York Buffalo, New York 14214, U.S.A NATIONALLICENCE 700 1- Krass S. School of Mathematics University of New South Wales Kensington, New South Wales 2033, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 44/3(1988-06), 311-323 1446-7887 44:3<311 1988 44 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 386307466 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge