Wolfgang M. Schmidt

Wolfgang M. Schmidt ( born October 3, 1933, Vienna) is an Austrian mathematician who deals with number theory.

Schmidt studied at the Vienna University of mathematics and physics. In 1955, he was there his doctorate under Edmund Hlawka with a thesis on the geometry of numbers (over higher critical determinants of star bodies ), which found its way into Cassels ' textbook Geometry of Numbers. 1956 to 1965 he was at the Universities of Vienna ( where he habilitated in 1960 ), the University of Montana, the University of Colorado and Columbia University. In 1965 he became a professor at the University of Colorado in Boulder, where he retired in 2001. 1970/71 he was at the Institute for Advanced Study.

1960 examined Schmidt, under what conditions, and numbers that are normal to the base, are also normal to the base, and showed: Just when is a rational number, any normal to the base number is also used to base normal ( is not a rational number, then, the set of numbers which are common in normal and not in the base, even the thickness of the continuum ). In 1968 he proved the existence of a number of T- class, introduced by Kurt Mahler class of transcendental numbers. Schmidt proved, among other things, the subspace theorem in diophantine approximations of the theory, from which also the set of Thue -Siegel -Roth follows. In the geometry of numbers, he improved the inequality in Minkowski Hlawka theorem. After Sergei Alexandrovich Stepanov had been in the 1960s an elementary proof of the Riemann 's conjecture for hyperelliptic curves ( originally by Andre Weil) simplified and extended Schmidt the proof. In a series of papers in the 1970s, he also dealt with the irregularities in the distribution of primes.

In 1972 he received the Cole prize in number theory. He is a member of the Austrian and Polish Academy of Sciences. He was three times (1970, 1974, 1983) Invited Speaker at the International Congress of Mathematicians (ICM ), 1974 he held the plenary (Application of Thue 's Method in various branches of number theory ).

In 2003 he received the Medal of Honour for Science and Art of the Republic of Austria. In 1986, he received the Humboldt Research Award. He holds honorary doctorates from the University of Ulm, the Sorbonne, the University of Waterloo and the University of Marburg. He is a Fellow of the American Mathematical Society.

Writings

  • Diophantine approximations and Diophantine equations. Lecture Notes in Mathematics 1467, Springer Verlag, 1991, reprint 1996, 2008 ISBN 978-3-540-54058-8
  • Equations over Finite Fields: An Elementary Approach. 2nd edition, Kendrick Press, 2004 ( first Lecture Notes in Mathematics, No. 536, 1976, Springer Verlag )
  • Approximation to algebraic numbers. L' Enseignement Mathematique Vol 17, 1971, p 187
Boulder (Colorado) Normal number Cardinality of the continuum Thue–Siegel–Roth theorem André Weil Mathematics Genealogy Project Integrated Authority File
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