Hall, R. R.; Huxley, M. N. Dedekind sums and continued fractions. (English) Zbl 0785.11027 Acta Arith. 63, No. 1, 79-90 (1993). P. Barkan [C. R. Acad. Sci., Paris, Sér. A 284, 923-926 (1977; Zbl 0347.10007)] has shown that the classical Dedekind sums \(s(p,q)\) can be evaluated in terms of quotients of convergents of the continued fraction for \(p/q\) by repeated use of the reciprocity law. This is an alternate form of the evaluation of \(s(p,q)\) in terms of the remainders in the Euclidean algorithm for the \(\text{gcd}(p,q)\) given in the reviewer’s Ph. D. dissertation in 1948 and published in [Modular functions and Dirichlet series in number theory (Graduate Texts Math. 41, Springer-Verlag) (1976; Zbl 0332.10017) (2nd ed. 1990) p. 73 (Exercise 20)]. This paper gives yet another evaluation based on continued fractions and Rademacher’s three-term relation for Dedekind sums. Reviewer: T.M.Apostol (Pasadena) Cited in 4 Documents MSC: 11F20 Dedekind eta function, Dedekind sums 11A55 Continued fractions Keywords:Dedekind sums; evaluation; continued fractions; Rademacher’s three-term relation Citations:Zbl 0347.10007; Zbl 0332.10017 PDFBibTeX XMLCite \textit{R. R. Hall} and \textit{M. N. Huxley}, Acta Arith. 63, No. 1, 79--90 (1993; Zbl 0785.11027) Full Text: DOI EuDML