Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T01:32:24.641Z Has data issue: false hasContentIssue false

Kurt Mahler, 1903–1988

Published online by Cambridge University Press:  09 April 2009

A. J. van der Poorten
Affiliation:
Alfred J. van der Poorten School of Mathematics, Physics, Computing and Electronics Macquarie UniversityNSW 2109, Australia
Rights & Permissions [Opens in a new window]

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Obituary
Copyright
Copyright © Australian Mathematical Society 1991

References

Baker, Alan (1966), ‘A note on the Padé tableK. Nederl. Akad. Wetensch. Proc. Ser. A 69, 596601CrossRefGoogle Scholar
Bombieri, E. and Schmidi, W. M. (1987), ‘On Thue's equationInvent. Math. 88, 6981CrossRefGoogle Scholar
David, W. Boyd (1981), ‘Speculations concerning the range of Mahler's measure’, Canad. Math. Bull. 24, 453469Google Scholar
Cassels, J. W. S. (1976), ‘An embedding theorem for fields’, Bull. Austral. Math. Soc. 14, 193198;CrossRefGoogle Scholar
Addendum: Bull. Austral. Math. Soc. 14, 479480CrossRefGoogle Scholar
Coates, John (1966), ‘On the algebraic approximation of functions I, II, III’, K. Nederl. Akad. Wetensch. Proc. Ser. A 69, 421461;CrossRefGoogle Scholar
On the algebraic approximation of functions IV’, K. Nederl. Akad. Wetensch. Proc. Ser. A 70 (1967), 205212CrossRefGoogle Scholar
Christol, G., Kamae, T., France, M. Mendès and Rauzy, G. (1980), ‘Suites algèbriques, automates et substitutions’, Bull. Soc. Math. France 108, 401419CrossRefGoogle Scholar
Cobham, A. (1968), ‘On the Hartmanis-Stearns problem for a class of tag machines’, Technical report RC 2178, IBM Research Centre, Yorktown Heights, New York, 15ppCrossRefGoogle Scholar
Dekking, Michel, France, Michel Mendès and van der Poorten, Alf (1982), ‘FOLDS!’, The Mathematical Intelligencer 4, 130138;CrossRefGoogle Scholar
II: ‘Symmetry disturbed’, The Mathematical Intelligencer 173181; III: ‘More morphisms’,Google Scholar
The Mathematical Intelligencer 190195Google Scholar
Davenport, H. (1958), ‘Indefinite quadratic forms in many variables (II)’, Proc. London Math. Soc. 8, 109126CrossRefGoogle Scholar
Dobrowolski, E. (1979), ‘On a question of Lehmer and the number of irreducible factors of a polynomial’, Acta Arith. 34, 391401CrossRefGoogle Scholar
Dubois, E. and Rhin, G. (1976), ‘Sur la majoration de formes linéaires à coefficients algébriques réels et p-adiques (Démonstration d'une conjecture de K. Mahler)’, C. R. Acad. Sc. Paris A282, 1211Google Scholar
Jan-Hendrik, Evertse (1984), ‘On sums of S-units and linear recurrences’, Compositio Math. 53, 225244Google Scholar
Evertse, J.-H., Györy, K., Stewart, C. L. and Tijdeman, R. (1988), ‘S-unit equations and their applications’, in New advances in transcendence theory ed. Baker, Alan, (Durham Symposium on Transcendental Number Theory 1986), Cambridge Univ. Press, 110174CrossRefGoogle Scholar
Hermite, C. (1873), ‘Sur la fonction exponentielle’, Oeuvres, t. III, 151181Google Scholar
Hermite, C. (1893), ‘Sur la généralization des fractions continues algébriques’, Oeuvres, t. IV, 357377Google Scholar
Jager, H. (1964), ‘A multidimensional generalization of the Padé table’, Proc. K. Nederl. Akad. v. Wetenschappen Series A 67, 192249Google Scholar
Jager, H., (1964), ‘A multidimensional generalization of the Padé table’, Proc. K. Nederl. Akad. v. Wetenschappen Series A 67, 192249Google Scholar
Khintchine, A. (1926), ‘Über eine Klasse linearer Diophantischer Approximationen’, Rend. Circ. Mat. Palermo 50, 170195CrossRefGoogle Scholar
Koksma, J. F. (1939), ‘Über die Mahlersche Klassenteilung der transzendenten Zahlen und die Approximation komplexer Zahlen durch algebraische Zahlen’, Monatsh. Math. Phys. 48, 176189CrossRefGoogle Scholar
Landau, E. (1905), ‘Sur quelques th´;orèmes de M. Petrovich relatifs aux zéros des fonctions analytiques’, Bull. Soc. Math. France 33, 251261CrossRefGoogle Scholar
Lech, Christer (1953), ‘A note on recurring series’, Ark. Mat. 2, 417421CrossRefGoogle Scholar
Lehmer, D. H. (1933), ‘Factorization of certain cyclotomic functions’, Ann. Math. 34, 461479CrossRefGoogle Scholar
LeVeque, W. J. (1961), Topics in Number Theory Vol. 2, Addison-WesleyGoogle Scholar
Lipshitz, L. and van der Poorten, A. J. (1990), ‘Rational functions, diagonals, automata and arithmetic’, in Number Theory, ed. Mollin, Richard A., (First Conference of the Canadian Number Theory Association, Banff 1988) Walter de Gruyter Berlin New York, 339358Google Scholar
Loxton, J. H. and van der Poorten, A. J. (1977a), ‘Arithmetic properties of certain functions in several variables III’, Bull. Austral. Math. Soc. 16, 1547CrossRefGoogle Scholar
Loxton, J. H. and van der Poorten, A. J. (1977b), ‘Transcendence and algebraic independence by a method of Mahler’, in Transcendence theory—advances and applications, ed. Baker, A. and Masser, D. W., Academic Press London and New York, Chapter 15, 211226Google Scholar
Loxton, J. H. and van der Poorten, A. J. (1988), ‘Arithmetic properties of automata: regular sequences’, J. für Math. 392, 5769Google Scholar
Margulis, G. A. (1987), ‘Formes quadratiques indéfinies et flots unipotents sur les espaces homogènesComptes Rendus Acad. Sci. Paris 304, 249253Google Scholar
Masser, D. W. (1982), ‘A vanishing theorem for power series’, Invent. Math. 67, 275296CrossRefGoogle Scholar
France, M. Mendès (1980), ‘Nombres algébriques et théorie des automates’, l'Ens. Math. (2) 26, 193199Google Scholar
Alfred, van der Poorten (1979), ‘A proof that Euler missed … Apéry's proof of the irrationality of ζ(3); An informal report’, The Mathematical Intelligencer 1, 195203Google Scholar
van der Poorten, A. J. (1989), ‘Some facts that should be better known; especially about rational functions’, in Number Theory and Applications, ed. Mollin, Richard A., (NATO - Advanced Study Institute, Banff, 1988) Kluwer Academic Publishers Dordrecht, 497528Google Scholar
van der Poorten, A. J. and Schlickewei, H. P. (1991), ‘Additive relations in number fields’, J. Austral. Math. Soc.CrossRefGoogle Scholar
Schlickewei, H. P. (1977a), ‘The p-adic Thue-Siegel-Roth-Schmidt theorem’, Arch. Mat. 29, 267270CrossRefGoogle Scholar
Schlickewei, H. P. (1977b), ‘Über die diophantische Gleichung x1 + x2 + … xn = 0Acta Arith. 33, 183185CrossRefGoogle Scholar
Schmidt, W. M. (1968), ‘T-number do exist, Symposia Mathematica IV INDAM, Rome Academic Press, London;Google Scholar
see also ‘Mahler's T-numbers’ Proc. Symposia in Pure Math. (Stonybrook 1969) XX Amer. Math. Soc., (1971), 275286Google Scholar
Schmidt, W. M. (1970), ‘Simultaneous approximation to algebraic numbers by rationalsActa Math. 125, 189201CrossRefGoogle Scholar
Schmidt, W. M. (1977), Small fractional parts of polynomials, CBMS Regional Conf. Ser. 32 Amer. Math. Soc., 41ppGoogle Scholar
Shidlovskii, A. B. (1959), ‘Transcendality and algebraic independence of the values of certain functions’, Amer. Math. Soc. Transl. (2) 27 (1963), 191230 = Trudy Moscov. Mat. Obsc. 8, 283–320; ‘A criterion for algebraic independence of the values of a class of entire functions’, Amer. Math. Soc. Transl. (2) 22 (1962), 339–370 = Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 35–66 and see further references in [200]Google Scholar
Siegel, C. L. (1929), ‘Über einige Anwendungen diophantischer Approximationen’, Preuß. Akad. Wiss. Phys.-mat. KI. Berlin No.1 = Gesammelte Abhandlungen I Springer Verlag (1966), 209266Google Scholar
Sprindzuk, V. G. (1965), ‘A proof of Mahler's conjecture on the measure of the set of S-numbers’, Izv. Akad. Nauk SSSR (ser. mat.) 29, 379436Google Scholar