Journal of the Ramanujan Mathematical Society

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Counting Diophantine Approximations of Small Height


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1 University of Colorado, Boulder, United States
     

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We will estimate the number of good approximations by algebraic numbers, in particular by algebraic numbers of small Height. As a consequence, we will be able to give new bounds for the number of “exceptional” approximations in Roth’s Theorem.
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  • Counting Diophantine Approximations of Small Height

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Authors

Wolfgang M. Schmidt
University of Colorado, Boulder, United States

Abstract


We will estimate the number of good approximations by algebraic numbers, in particular by algebraic numbers of small Height. As a consequence, we will be able to give new bounds for the number of “exceptional” approximations in Roth’s Theorem.