A problem of Mahler on farctional parts of powers of an algebraic number is solved, namely a classification is provided of the algebraic numbers $\alpha$ such that the fractional powers of $\alpha^n$ tends to zero exponentially on a sequence of integers. A problem of Mendes France is solved, by proving that the period length of the continued fraction of the powers of a quadratic irrational tends to infinity apart trivial cases.
On the rational approximations to the powers of an algebraic number. Solution of two problems by Mahler and Mendes France
CORVAJA, Pietro;
2004-01-01
Abstract
A problem of Mahler on farctional parts of powers of an algebraic number is solved, namely a classification is provided of the algebraic numbers $\alpha$ such that the fractional powers of $\alpha^n$ tends to zero exponentially on a sequence of integers. A problem of Mendes France is solved, by proving that the period length of the continued fraction of the powers of a quadratic irrational tends to infinity apart trivial cases.File in questo prodotto:
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