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Irrationality Exponents.pdf

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🔗 Source: danielduverney.fr
📊 Size: 185 KB
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Summary

The irrationality exponent of numbers related to Cahen's constant is estimated using lower and upper bounds for the irrationality exponent of general continued fractions under certain conditions. The numbers γl,ε and ξε are defined in terms of the sequences un = un(ε) and are expanded in continued fractions. Theorem 1 states that µ(γ1,ε) = 3 and provides bounds for µ(γl,ε) for l ≥ 2. Corollaries 1 and 2 show that γl,ε and ξε are non-Liouville transcendental numbers. Examples of these numbers are given, including Cahen's constant and the sum of reciprocals of Fermat numbers. Theorem 2 provides bounds for the irrationality exponent of general continued fractions, which is used to prove Theorem 1. An alternative proof of µ(γ1,ε) = 3 is given using approximations by truncated sums.

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The irrationality exponent of numbers related to Cahen's constant is estimated using lower and upper bounds for the irrationality exponent of general continued...

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  • File Format: PDF
  • File Size: 185 KB
  • Pages: 19
  • Language: EN
  • Total Downloads: 235
  • Last Updated: 1 week ago

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