Wolfgang Schmidt (mathematician)

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

Wolfgang Schmidt, Oberwolfach 2007

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

1960 examined Schmidt, under what conditions and numbers to base normal are also the base are normal, and showed: Just when a rational number, each to the base is normal number also to the base (normal is not a rational number , then the set of numbers that are normal in and not normal in the base has even the width of the continuum ). In 1968 he proved the existence of a number of the T-class, a class of transcendent numbers introduced by Kurt Mahler . Schmidt proved, among other things, the subspace theorem in the theory of Diophantine approximations, from which the Thue-Siegel-Roth theorem follows. In the geometry of numbers, he improved the inequality in the Minkowski-Hlawka theorem. After Sergei Alexandrowitsch Stepanow had given an elementary proof of the Riemann conjecture for hyperelliptic curves in the 1960s (originally by André Weil ), Schmidt simplified and expanded the proof. In a series of works in the 1970s, he also dealt with the irregularities in the distribution of prime numbers. ${\displaystyle r}$ ${\displaystyle s}$ ${\displaystyle r}$ ${\displaystyle s}$ ${\displaystyle \ln(r)/\ln(s)}$ ${\displaystyle r}$ ${\displaystyle s}$ ${\displaystyle \ln(r)/\ln(s)}$ ${\displaystyle r}$ ${\displaystyle s}$

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

Wolfgang Schmidt, Vienna 1987

In 2003 he received the Decoration of Honor for Science and Art of the Republic of Austria . In 1986 he received the Humboldt Research Award. He is honorary doctor of the University of Ulm, the Sorbonne, the University of Waterloo and the University of Marburg. He is a fellow of the American Mathematical Society and the American Academy of Arts and Sciences .

Fonts

• 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

Web links

• Golden jubilee at the University of Vienna for Schmidt
• Conversation with Schmidt (video)
• Wolfgang Schmidt in the Mathematics Genealogy Project (English)

Individual evidence

1. ↑ Wolfgang M. Schmidt: On normal numbers , Pacific Journal of Mathematics 10, 1960, pp. 661-672 ( online , ZMath Review )
2. ↑ Wolfgang M. Schmidt: Norm form equations , The Annals of Mathematics 96, 1972, pp. 526-551 ( ZMath author's lecture )
3. ↑ Illinois J. Math., Vol. 7, 1963, pp. 18-23
4. ↑ Schmidt Equations over finite fields , 1976, Lecturenotes in Mathematics
5. ^ Lecture Some recent progress in diophantine approximations
6. ↑ Lecture Analytic methods for congruences, diophantine equations and approximations