An elliptic analogue of the multiple Dedekind sums

Shigeki Egami

Compositio Mathematica (1995)

  • Volume: 99, Issue: 1, page 99-103
  • ISSN: 0010-437X

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Egami, Shigeki. "An elliptic analogue of the multiple Dedekind sums." Compositio Mathematica 99.1 (1995): 99-103. <http://eudml.org/doc/90409>.

@article{Egami1995,
author = {Egami, Shigeki},
journal = {Compositio Mathematica},
keywords = {elliptic analogue of multiple Dedekind sums; reciprocity law},
language = {eng},
number = {1},
pages = {99-103},
publisher = {Kluwer Academic Publishers},
title = {An elliptic analogue of the multiple Dedekind sums},
url = {http://eudml.org/doc/90409},
volume = {99},
year = {1995},
}

TY - JOUR
AU - Egami, Shigeki
TI - An elliptic analogue of the multiple Dedekind sums
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 99
IS - 1
SP - 99
EP - 103
LA - eng
KW - elliptic analogue of multiple Dedekind sums; reciprocity law
UR - http://eudml.org/doc/90409
ER -

References

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  1. [Ber] Berndt, B.C.: Reciprocity theorems of Dedekind sums and generalization, Advance in Math.23 (1977), 285-316. Zbl0342.10014MR429711
  2. [Ca1] Carlitz, L.: A note on generalized Dedekind sums, Duke Math. J.21 (1954), 399-403. Zbl0057.03802MR62766
  3. [Ca2] Carlitz, L.: Many term relations for multiple Dedekind sums. Indian J. Math.20 (1978), 77-89. Zbl0418.10013MR603918
  4. [E-Z] Eichler, M. and Zagier, D.: The Theory of Jacobi Forms, Progress in Math.55, Birkhäuser, 1985. Zbl0554.10018MR781735
  5. [HBJ] Hirzebruch, F., Berger, T. and Jung, R.: Manifolds and Modular forms, Aspects of Math. E.20, Vieweg, 1992. Zbl0767.57014MR1189136
  6. [H-Z] Hirzebruch, F. and Zagier, D.: The Atiyah-Singer Theorem and Elementary Number Theory, Math. Lecture Series3, Publish or Perish Inc., 1974. Zbl0288.10001MR650832
  7. [It1] Ito, H.: A function on the upper half space which is analogous to imaginary part of log η(z), J. reine angew. Math.373 (1987), 148-165. Zbl0601.10021
  8. [It2] Ito, H.: On a property of elliptic Dedekind sums, J. Number Th.27 (1987), 17-21. Zbl0624.10018MR904003
  9. [Scz] Sczech, R.: Dedekindsummen mit elliptischen Functionen, Invent. Math.76 (1984), 523-551. Zbl0521.10021MR746541
  10. [Za1] Zagier, D.: Higher order Dedekind sums, Math. Ann.202 (1973), 149-172. Zbl0237.10025MR357333
  11. [Za2] Zagier, D.: Equivariant Pontrjagin Classes and Application to Orbit Spaces, Lecture Note in Math. 290, Springer, 1972. Zbl0238.57013MR339202

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