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Generalizations of Knopp's Identity

✍ Scribed by Beifang Chen; Zhi-Wei Sun

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
128 KB
Volume
97
Category
Article
ISSN
0022-314X

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✦ Synopsis

For integers a; b and n > 0 we define S G ða; b; nÞ ¼ X nÀ1 r¼0 n[br ar n ln G br n and T G ða; b; nÞ ¼ X nÀ1 r¼0 n[br ar n G 0 ðfbr=ngÞ Gðfbr=ngÞ ; which are similar to the homogeneous Dedekind sum Sða; b; nÞ: In this paper we establish functional equations for S G and T G : Moreover, by means of uniform function (introduced by Sun in 1989) we are able to extend Knopp's identity on Dedekind sums vastly.

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