In 1960, he proved that every normal number in base r is normal in base s if and only if log r / log s is a rational number. He also proved the existence of T numbers. His series of papers on irregularities of distribution contained landmark results; see J.Beck and W.Chen, Irregularities of Distribution, Cambridge University Press, for more information.Schmidt is in a small group of number theorists who have been invited to address the International Congress of Mathematicians three times. The others are Iwaniec, Shimura, and Tate.
Books
Diophantine approximation. Lecture Notes in Mathematics 785. Springer. (1980 )
Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, Springer Verlag 2000
Equations Over Finite Fields: An Elementary Approach, 2nd edition, Kendrick Press 2004
On normal numbers. Pacific Journal of Mathematics, 10:661-672, 1960.
References
Further reading
, Wolfgang M. Schmidt, H. P. Schlickewei, Robert F. Tichy, Klaus Schmidt,......