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Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functions

M. Can|M. Cenkci|V. Kurt|Y. Simsek
장전수학회 (Jangjeon Mathematical Society)|2009.04|Advanced Studies in Contemporary Mathematics|제18권 제2호|pp. 135-160

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참고문헌

키워드

Barnes' type multiple Frobenius-Euler l-functionsBernoulli polynomials and functionsDedekind sums.
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초록

The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes' type multiple Frobenius-Euler numbers and polynomials. By applying Mellin transformation to these functions, we de¯ne Barnes' type multiple l-functions, which interpolate Frobenius-Euler numbers at negative integers. By using generalizations of the Frobenius-Euler functions, we de¯ne generalized Dedekind type sums and prove corresponding reciprocity law. We also give twisted versions of the Frobenius-Euler polynomials and new Dedekind type sums and corresponding reciprocity law. Furthermore, by using p-adic q-Volkenborn integral and twisted (h,q)-Bernoulli functions, we construct p-adic (h,q)-higher order Dedekind type sums. By using relation between Bernoulli and Frobenius-Euler functions, we also de¯ne analogues of Hardy-Berndt type sums. We give some new relations related to to these sums as well.

Abstract

The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes' type multiple Frobenius-Euler numbers and polynomials. By applying Mellin transformation to these functions, we de¯ne Barnes' type multiple l-functions, which interpolate Frobenius-Euler numbers at negative integers. By using generalizations of the Frobenius-Euler functions, we de¯ne generalized Dedekind type sums and prove corresponding reciprocity law. We also give twisted versions of the Frobenius-Euler polynomials and new Dedekind type sums and corresponding reciprocity law. Furthermore, by using p-adic q-Volkenborn integral and twisted (h,q)-Bernoulli functions, we construct p-adic (h,q)-higher order Dedekind type sums. By using relation between Bernoulli and Frobenius-Euler functions, we also de¯ne analogues of Hardy-Berndt type sums. We give some new relations related to to these sums as well.

참고문헌 (53)

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