Rational approximations of the exponential function at rational points

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  • Kalle Leppälä
  • Tapani Matala-aho, Oulun Yliopisto
  • ,
  • Topi Törmä, Oulun Yliopisto

We give explicit and asymptotic lower bounds for the quantity |es/t−M/N| by studying a generalized continued fraction expansion of es/t. In cases |s|≥3 we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.

Original languageEnglish
JournalJournal of Number Theory
Pages (from-to)220-239
Number of pages20
Publication statusPublished - 1 Oct 2017

    Research areas

  • Diophantine approximation, Generalized continued fraction, Irrationality measure

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