Quadratic irrational integers with partly prescribed continued fraction expansion

2004/10/31 by Alfred J. van der Poorten, van der Poorten, Alfred J. · 1 citation
Mathematics · #111A65 11J68 (primary) #11J70 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:111A65 #msc:11J68 #msc:11J70

paper · pdf · doi:10.48550/arxiv.math/0411005

10 pages; dedicated to the memory of Bela Brindza

arxiv created 2004/10/31 · arxiv updated 2009/12/01

Abstract

We generalise remarks of Euler and of Perron by explaining how to detail all quadratic irrational integers for which the symmetric part of the period of their continued fraction expansion commences with prescribed partial quotients. The function field case is particularly striking.

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