Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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THE PARITIES OF CONTINUED FRACTION

  • Ahn, Young-Ho (Department of Mathematics, Mokpo National University)
  • Received : 2008.11.06
  • Accepted : 2008.11.25
  • Published : 2008.12.25
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Abstract

Let T be Gauss transformation on the unit interval defined by T (x) = ${\frac{1}{x}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.

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