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10 - Mathematical Sciences
University of Liverpool
Geometry of Continued Fractions
This research monograph contains both a review of previously published material and new original research. The major new contributions of the book are as follows:
a) Previously unpublished results of Gauss Reduction Theory in three dimensions are presented in Chapter 21 (pp. 326-344) for the first time.
b) New approximation methods for geometric objects such as lines, planes and cones are developed in Chapter 10 (pp. 117-136) . This is the second step in a general program on maximal commutative subgroup approximation announced by the author together with A.Vershik.
These are perhaps the most substantial new research contribution in the book, but Chapter 14.4 (pp. 198-204) also constitutes new research. Some other minor new results can be found throughout the book, but we do not ask for these to be reviewed as part of the REF process.
