An elliptic analogue of the multiple Dedekind sums

Shigeki Egami

Compositio Mathematica (1995)

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

How to cite


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

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 = {},
volume = {99},
year = {1995},

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 -
ER -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.