Thus Diophantine approximations and transcendental number theory are very close areas that share many theorems and methods.
12.
Littlewood's collaborative work, carried out by correspondence, covered fields in Diophantine approximation and Waring's problem, in particular.
13.
The outstanding works of Klaus Roth and Alan Baker exemplify what this can do, in diophantine approximation.
14.
In 1986, Margulis gave a complete resolution of the Oppenheim conjecture on quadratic forms and diophantine approximation.
15.
With Elon Lindenstrauss and Manfred Einsiedler, Katok made important progress on the Littlewood Conjecture in the theory of Diophantine approximations.
16.
This apparently trivial remark is used in almost every proof of lower bounds for Diophantine approximations, even the most sophisticated ones.
17.
He completed his Ph . D . thesis, " On the Hardy-Littlewood Problem of Diophantine Approximations and Its Generalizations, " in 1939.
18.
One may also study real numbers in relation to rational numbers, e . g ., as approximated by the latter ( Diophantine approximation ).
19.
Applications of " p "-adic analysis have mainly been in number theory, where it has a significant role in diophantine geometry and diophantine approximation.
20.
One may also note that the exponent 1 + 1 / " n " + ? is best possible by Dirichlet's theorem on diophantine approximation.
