Properties of certain integer-valued analogues of Dedekind sums

Jeffrey L. Meyer

Acta Arithmetica (1997)

  • Volume: 82, Issue: 3, page 229-242
  • ISSN: 0065-1036

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Jeffrey L. Meyer. "Properties of certain integer-valued analogues of Dedekind sums." Acta Arithmetica 82.3 (1997): 229-242. <http://eudml.org/doc/207089>.

@article{JeffreyL1997,
author = {Jeffrey L. Meyer},
journal = {Acta Arithmetica},
keywords = {Dedekind sums; reciprocity laws},
language = {eng},
number = {3},
pages = {229-242},
title = {Properties of certain integer-valued analogues of Dedekind sums},
url = {http://eudml.org/doc/207089},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Jeffrey L. Meyer
TI - Properties of certain integer-valued analogues of Dedekind sums
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 3
SP - 229
EP - 242
LA - eng
KW - Dedekind sums; reciprocity laws
UR - http://eudml.org/doc/207089
ER -

References

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  1. [1] T. Asai, Some arithmetic on Dedekind sums, J. Math. Soc. Japan 38 (1986), 163-172. Zbl0571.10010
  2. [2] B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine Angew. Math. 303/304 (1978), 332-365. Zbl0384.10011
  3. [3] R. Dedekind, Erläuterungen zu zwei Fragmenten von Riemann, in: Riemann's Gesammelte Math. Werke, 2nd ed., 1882, 466-472. 
  4. [4] W. Duke, J. B. Friedlander and H. Iwaniec, Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math. 141 (1995), 423-441. Zbl0840.11003
  5. [5] L. A. Goldberg, Transformations of theta-functions and analogues of Dedekind sums, thesis, Univ. of Illinois, Urbana, 1981. 
  6. [6] G. H. Hardy, On certain series of discontinuous functions connected with the modular functions, Quart. J. Math. Oxford 36 (1905), 93-123. Zbl35.0468.03
  7. [7] G. H. Hardy, Collected Papers, Vol. IV, Clarendon Press, Oxford, 1969. Zbl0181.28902
  8. [8] D. Hickerson, Continued fractions and density results for Dedekind sums, J. Reine Angew. Math. 290 (1977), 113-116. Zbl0341.10012
  9. [9] J. L. Meyer, Analogues of Dedekind sums, thesis, Univ. of Illinois, Urbana, 1997. 
  10. [10] I. Niven, H. Zuckerman and H. Montgomery, An Introduction to the Theory of Numbers, 5th ed., Wiley, 1991. Zbl0742.11001
  11. [11] L. Pinzur, On a question of Rademacher concerning Dedekind sums, Proc. Amer. Math. Soc. 61 (1976), 11-15. Zbl0314.10002
  12. [12] H. Rademacher, Zur Theorie der Dedekindschen Summen, Math. Z. 63 (1956), 445-463. 
  13. [13] H. Rademacher, Questions 99 and 100, in: Proc. 1963 Number Theory Conference, Univ. of Colorado, Boulder, Colo., 1963, 112. 
  14. [14] K. Rosen, On the sign of some Dedekind sums, J. Number Theory 9 (1977), 209-212. Zbl0349.10005
  15. [15] R. Sitaramachandrarao, Dedekind and Hardy sums, Acta Arith. 48 (1987), 325-340. Zbl0635.10002

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