In 1970 he was an Invited Speaker at the ICM in Nice with talk " New applications of analytic and p-adic methods in diophantine approximations ".
22.
He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem.
23.
For upper bounds, one has to take into account that not all the " best " Diophantine approximations provided by the convergents may have the desired accuracy.
24.
Additional subjects of St�rmer's mathematical research included Lie groups, the gamma function, and Diophantine approximation of algebraic numbers and of the transcendental numbers arising from elliptic functions.
25.
Ergodic theory has fruitful connections with harmonic analysis, Lie theory ( representation theory, lattices in algebraic groups ), and number theory ( the theory of diophantine approximations, L-functions ).
26.
The study of the properties of unipotent and quasiunipotent flows on homogeneous spaces remains an active area of research, with applications to further questions in the theory of Diophantine approximation.
27.
The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity.
28.
A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in diophantine approximation.
29.
Siegel's result was ineffective ( see effective results in number theory ), since Thue's method in diophantine approximation also is ineffective in describing possible very good rational approximations to algebraic numbers.
30.
The obvious measure of the accuracy of a Diophantine approximation of a real number by a rational number is \ left | \ alpha-\ frac { p } { q } \ right |.
