Seminars

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For any real irrational number alpha, Dirichlet's theorem guarantees that there are infinitely many rational p/q, such that |alpha - p/q|<1/q^2. Moreover, there are real numbers (with irrationality measure 2) for which this approximation cannot be improved. The same holds true for approximation of real numbers by elements of any fixed totally real field. In this talk, we shall discuss the question of whether it is possible to obtain better approximations of real numbers over infinite totally real extensions. In particular, we prove such a result for totally p-adic real extensions. This is work in progress with Sushant Kala.

Chennai Combinatorics Colloquium Talk, organized in collaboration with IIT Madras, CMI, ISI Chennai and Krea University.

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