Reciprocity formulae for general Dedekind-Rademacher sums

R. R. Hall; J. C. Wilson; D. Zagier

Acta Arithmetica (1995)

  • Volume: 73, Issue: 4, page 389-396
  • ISSN: 0065-1036

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R. R. Hall, J. C. Wilson, and D. Zagier. "Reciprocity formulae for general Dedekind-Rademacher sums." Acta Arithmetica 73.4 (1995): 389-396. <http://eudml.org/doc/206830>.

@article{R1995,
author = {R. R. Hall, J. C. Wilson, D. Zagier},
journal = {Acta Arithmetica},
keywords = {general Dedekind-Rademacher sums; Bernoulli polynomial; reciprocity theorem},
language = {eng},
number = {4},
pages = {389-396},
title = {Reciprocity formulae for general Dedekind-Rademacher sums},
url = {http://eudml.org/doc/206830},
volume = {73},
year = {1995},
}

TY - JOUR
AU - R. R. Hall
AU - J. C. Wilson
AU - D. Zagier
TI - Reciprocity formulae for general Dedekind-Rademacher sums
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 4
SP - 389
EP - 396
LA - eng
KW - general Dedekind-Rademacher sums; Bernoulli polynomial; reciprocity theorem
UR - http://eudml.org/doc/206830
ER -

References

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  1. [1] T. M. Apostol, Generalized Dedekind sums and the transformation formulae of certain Lambert series, Duke Math. J. 17 (1950), 147-157. Zbl0039.03801
  2. [2] B. C. Berndt, Reciprocity theorems for the Dedekind sums and generalizations, Adv. in Math. 23 (1977), 285-316. Zbl0342.10014
  3. [3] L. Carlitz, Some theorems on generalized Dedekind sums, Pacific J. Math. 3 (1953), 513-522. Zbl0057.03701
  4. [4] L. Carlitz, A three-term relation for Dedekind-Rademacher sums, Publ. Math. Debrecen 14 (1967), 119-124. Zbl0167.31403
  5. [5] R. Dedekind, Erläuterungen zu den Fragmenten XXVIII, in: B. Riemann's Gesammelte mathematische Werke, 2nd ed., Teubner, Leipzig, 1892, 466-478. 
  6. [6] 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. Zbl0783.11021
  7. [7] M. Mikolás, On certain sums generating the Dedekind sums and their reciprocity laws, Pacific J. Math. 7 (1957), 1167-1178. Zbl0081.04302
  8. [8] J. L. Raabe, Zurückführung einiger Summen und bestimmten Integrale auf die Jacob-Bernoullische Funktion, J. Reine Angew. Math. 42 (1851), 348-367. 
  9. [9] H. Rademacher, Generalization of the reciprocity formula for Dedekind sums, Duke Math. J. 21 (1954), 391-397. Zbl0057.03801
  10. [10] H. Rademacher and E. Grosswald, Dedekind Sums, Carus Math. Monographs 16, Math. Assoc. Amer., 1972. 
  11. [11] L. Takács, On generalized Dedekind sums, J. Number Theory 11 (1979), 264-272. Zbl0404.10006
  12. [12] J. C. Wilson, D. Phil. Thesis, University of York, United Kingdom, 1993. 

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