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A note on the modified \(q\)-Dedekind sums. (English) Zbl 1310.11048

Summary: In the present paper, the fundamental aim is to consider a \(p\)-adic continuous function for an odd prime to inside a \(p\)-adic \(q\)-analogue of the higher order extended Dedekind-type sums related to \(q\)-Genocchi polynomials with weight alpha by using fermionic \(p\)-adic invariant \(q\)-integral on \(\mathbb Z_p\).

MSC:

11F20 Dedekind eta function, Dedekind sums
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
11B68 Bernoulli and Euler numbers and polynomials
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