Analytic Theory of Continued Fractions III Proceedings of a Seminar-
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1406 L. Jacobsen (Ed.)
Analytic Theory of Continued Fractions III Proceedings of a Seminar-Workshop, held in Redstone, USA, June 26-July 5,1988
Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong
Editor
Lisa Jacobsen Division of Mathematical Sciences University of Trondheim N-7034 Trondheim, Norway
Mathematics Subject Classification (1980): 01A55, 10A32, 10F35, 30B70, 33A30, 34A50, 40A 15,41 A21 ISBN 3-540-51830-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51830-4 Springer-Verlag New York Berlin Heidelberg
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PREFACE
This volume contains the proceedings of a research Seminar-Workshop held in Redstone, Colorado from June 26 to July 5, 1988. The topic of this workshop was Analytic Theory of Continued Fractions, and it was organized by William B. Jones, University of Colorado and Arne Magnus, Colorado State University.
This was the third workshop of its kind. The first one was held in Loen , Norway in 1981 (proceedings published in LN in M NO 932), the second one in Pitlochry and Aviemore, Scotland in 1985 (proceedings published in LN in M NO 1199). The idea is that workers in the field shall come together to exchange ideas and start cooperation. So, in addition to the presentation of our latest results, we have talks on ideas, half-finished projects, ideas that did not work, etc. Questions and comments, stupid or not, are encouraged.
This time analysis of papers from the turn of the century was one of the issues. Mathematicians like Helge von Koch, Jan Sleszynski and Julius Worpitzky had results and arguments which still deserve attention. Indirectly, these studies led to the study of separate convergence, a topic presented in a survey article in this velum, and to a historical article on Julius Worpitzky. In addition we continued discussions on nearness problems, the connection to Pade Approximants, and applications to number theory and differential equations. Interesting in this respect is for instance the use of Lange's O-fractions to solve Riccati equations, and the question of finding thin subsets Eo of an element region E whose best limit region V0 is dense in the best limit region V for E. Also several other topics which are not reflected in these proceedings were discussed and will hopefully be published elsewhere.
It is evident that for workshops
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