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Search Results (2)

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Keywords = twisted (h, q)-Bernoulli polynomials

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9 pages, 272 KiB  
Article
p-Adic q-Twisted Dedekind-Type Sums
by Abdelmejid Bayad and Yilmaz Simsek
Symmetry 2021, 13(9), 1756; https://doi.org/10.3390/sym13091756 - 20 Sep 2021
Cited by 2 | Viewed by 2345
Abstract
The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral and the Teichmüller character representations of the Bernoulli polynomials, we give reciprocity law of these sums. These sums and their reciprocity law generalized [...] Read more.
The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral and the Teichmüller character representations of the Bernoulli polynomials, we give reciprocity law of these sums. These sums and their reciprocity law generalized some of the classical p-adic Dedekind sums and their reciprocity law. It is to be noted that the Dedekind reciprocity laws, is a fine study of the existing symmetry relations between the finite sums, considered in our study, and their symmetries through permutations of initial parameters. Full article
(This article belongs to the Special Issue Recent Advances in Number Theory and Their Applications)
19 pages, 339 KiB  
Article
Multiple Dedekind Type Sums and Their Related Zeta Functions
by Abdelmejid Bayad and Yilmaz Simsek
Mathematics 2021, 9(15), 1744; https://doi.org/10.3390/math9151744 - 24 Jul 2021
Cited by 2 | Viewed by 1634
Abstract
The main purpose of this paper is to use the multiple twisted Bernoulli polynomials and their interpolation functions to construct multiple twisted Dedekind type sums. We investigate some properties of these sums. By use of the properties of multiple twisted zeta functions and [...] Read more.
The main purpose of this paper is to use the multiple twisted Bernoulli polynomials and their interpolation functions to construct multiple twisted Dedekind type sums. We investigate some properties of these sums. By use of the properties of multiple twisted zeta functions and the Bernoulli functions involving the Bernoulli polynomials, we derive reciprocity laws of these sums. Further developments and observations on these new Dedekind type sums are given. Full article
(This article belongs to the Section A: Algebra and Logic)
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