Abstract: We discuss a folklore result from the theory of (not necessarily regular) continued fractions, known as Folding Lemma. The lemma states that adding some special term to a finite continued fraction leads to a new continued fraction with an almost symmetric pattern in it. This easy observation has many number-theoretical corollaries.
In this talk we will focus on how does the Folding lemma help in constructing transcendental numbers, constructing numbers from a Cantor set with a prescribed irrationality exponent, getting bounds in Zaremba’s conjecture and proving some results about the Minkowski question mark function.
Folding lemma and its applications in Number Theory
05.11.2024 15:00 - 16:30
Organiser:
I. Fischer (U Wien), M. Schlosser (U Wien)
Location: