The Petersson–Knopp Identity for the Homogeneous Dedekind Sums

✍ Scribed by Zhiyong Zheng

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 273 KB
• Volume: 57
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0045

✦ Synopsis

It is the generalization of Knopp's identity for homogeneous Dedekind sums.

1996 Academic Press, Inc.

where ((x))=x&[x]& 1 2 if x{integer, ((x))=0 otherwise, and _(n) is the sum of the positive divisors of n.

Knopp's identity is valid for arbitrary integers a and q with q>0, and his derivation uses the functional equation for Dedekind's eta-function '({) article no.