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The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions
Author(s) -
Beardon Alan F.,
Short Ian
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq006
Subject(s) - mathematics , stern , conformal map , pure mathematics , group (periodic table) , space (punctuation) , mathematical analysis , quantum mechanics , physics , computer science , marine engineering , engineering , operating system
We unify and extend three classical theorems in continued fraction theory, namely the Stern–Stolz Theorem, the Seidel–Stern Theorem and Van Vleck's Theorem. Our arguments use the group of Möbius transformations both as a topological group and as the group of conformal isometries of three‐dimensional hyperbolic space.