A three variable identity connected with Dedekind sums

1995 ◽  
Vol 30 (3) ◽  
pp. 189-203
Author(s):  
R. R. Hall ◽  
M. N. Huxley ◽  
J. C. Wilson
Keyword(s):  
Dedekind Sums ◽  
Variable Identity

scholarly journals Identities on poly-Dedekind sums

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Hyunseok Lee ◽  
Lee-Chae Jang
Keyword(s):  
Modular Group ◽  
Reciprocity Relation ◽  
Dedekind Sums ◽  
Transformation Behavior ◽  
Dedekind Eta Function ◽  
Bernoulli Function ◽  
Bernoulli Functions

Abstract Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider the poly-Dedekind sums obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.

Dedekind sums and the signature of f (x, y) + z N , II

1999 ◽  
Vol 5 (1) ◽  
pp. 161-179 ◽  
Author(s):  
A. Némethi
Keyword(s):  
Dedekind Sums

scholarly journals A theorem on generalized Dedekind sums

1965 ◽  
Vol 11 (2) ◽  
pp. 253-260 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Dedekind Sums

scholarly journals Generalizations of Dedekind sums and their reciprocity laws

2003 ◽  
Vol 106 (4) ◽  
pp. 355-378 ◽  
Author(s):  
Yumiko Nagasaka ◽  
Kaori Ota ◽  
Chizuru Sekine
Keyword(s):  
Dedekind Sums ◽  
Reciprocity Laws

scholarly journals Notes on generalized Dedekind sums

1977 ◽  
Vol 33 (4) ◽  
pp. 297-325 ◽  
Author(s):  
Donald Knuth
Keyword(s):  
Dedekind Sums
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