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Title: Has material I haven't found in any other book
Review: There are several good books on continued fractions, in particular the chapter on continued fractions in Hardy and Wright, and Khinchin's book. But these books don't have the material Lang does on asymptotic approximations. The material I like in Lang's book is in the second and third chapters, where he proves results like estimating the number of integers so that certain remainders modulo 1 are less than a certain size, or estimating the sum of reciprocals of remainders. However I'm not happy with the proofs that I've read in detail, like the lemma on p. 39. A careful reader can probably rewrite most proofs in the book to make them understandable. Lang tries to avoid writing out some ugly details that would really help someone unfamiliar with the subject understand the proofs. At least Lang writes precisely if not carefully.
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