Reciprocity formulae for general Dedekind-Rademacher sums

ArticleOriginal scientific text

Title

Authors ¹, ¹, ²

Department of Mathematics, University of York, York YO1 5DD, United Kingdom
Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, 53225 Bonn, Germany

T. M. Apostol, Generalized Dedekind sums and the transformation formulae of certain Lambert series, Duke Math. J. 17 (1950), 147-157.
B. C. Berndt, Reciprocity theorems for the Dedekind sums and generalizations, Adv. in Math. 23 (1977), 285-316.
L. Carlitz, Some theorems on generalized Dedekind sums, Pacific J. Math. 3 (1953), 513-522.
L. Carlitz, A three-term relation for Dedekind-Rademacher sums, Publ. Math. Debrecen 14 (1967), 119-124.
R. Dedekind, Erläuterungen zu den Fragmenten XXVIII, in: B. Riemann's Gesammelte mathematische Werke, 2nd ed., Teubner, Leipzig, 1892, 466-478.
R. R. Hall and J. C. Wilson, On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums, Math. Proc. Cambridge Philos. Soc. 114 (1993), 9-24.
M. Mikolás, On certain sums generating the Dedekind sums and their reciprocity laws, Pacific J. Math. 7 (1957), 1167-1178.
J. L. Raabe, Zurückführung einiger Summen und bestimmten Integrale auf die Jacob-Bernoullische Funktion, J. Reine Angew. Math. 42 (1851), 348-367.
H. Rademacher, Generalization of the reciprocity formula for Dedekind sums, Duke Math. J. 21 (1954), 391-397.
H. Rademacher and E. Grosswald, Dedekind Sums, Carus Math. Monographs 16, Math. Assoc. Amer., 1972.
L. Takács, On generalized Dedekind sums, J. Number Theory 11 (1979), 264-272.
J. C. Wilson, D. Phil. Thesis, University of York, United Kingdom, 1993.