Pacific Journal of Mathematics

On certain sums generating the Dedekind sums and their reciprocity laws.

M. Mikolás

Article information

Source
Pacific J. Math., Volume 7, Number 2 (1957), 1167-1178.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103043508

Mathematical Reviews number (MathSciNet)
MR0091303

Zentralblatt MATH identifier
0081.04302

Subjects
Primary: 10.1X

Citation

Mikolás, M. On certain sums generating the Dedekind sums and their reciprocity laws. Pacific J. Math. 7 (1957), no. 2, 1167--1178. https://projecteuclid.org/euclid.pjm/1103043508


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References

  • [2] , Theorems on generalized Dedekind sums, Pacific J. Math., 2 (1952), 1-9.
  • [3] L. Carlitz, Some theorems on generalized Dedekind sums, Pacific J. Math., 3 (1953), 513-522.
  • [4] L. Carlitz,The reciprocity theorem for Dedekind sums, Pacific J. Math., 3 (1953),523- 527.
  • [5] L. Carlitz, Duke Math. J., 21 (1954),399-403.
  • [6] L. Carlitz, Dedekind sums and Lambert series, Proc. Amer. Math. Soc, 5 (1954), 580- 584.
  • [7] R. Dedekind, Erlauterungen zu Riemann's Fragmenten 'ber die Grenzfalle der el- liptischen Funktionen, Gesammelte mathematische Werke, vol. 1, Braunschweig, 1930,159- 173.
  • [8] L. J. Mordell, The reciprocity formula for Dedekind sums, Amer. J. Math. 73 (1951), 593-598.
  • [9] H. Rademacher, Zur Theorie der Modulfunktionen, J. Reine Angew. Math., 167 (1932), 312-336.
  • [10] H. Rademacher, Die Reziprozitatsformel fur Dedekindsche Summen, Acta Sci. Math. Szeged, 12B (1950), 57-60. II., Generalization of the reciprocity formula for Dedekind sums, Duke Math. J., 21 (1954), 391-397.
  • [12] H. Rademacher and A. Whiteman, Theorems on Dedekind sums, Amer. J. Math., 63 (1941), 377-407.
  • [13] L. Redei, Elementarer Beweis und Verallgemeinerung einer Reziprozitatsformelvon Dedekind, Acta Sci. Math. Szeged, 12B (1950), 236-239.