Arithmetic Study Group: Diagonal approximation in completions of the rationals
21 October 2014 14:00 in CM103
If classical Diophantine approximation aims to give quantitative versions of the statement "the rationals are dense in the reals", then diagonal Diophantine approximation can be thought of as trying to give quantitative version of the weak approximation theorem. In its most basic form (with the rational numbers as the ground field), the weak approximation theorem states that if we take elements from finitely many distinct completions of the rationals, we can always find a sequence of rationals which approaches each of them simultaneously.
We explain the general setup of diagonal Diophantine approximation, and sketch proofs of some of the main results in the setting of diagonal approximation over the rationals.
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