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Russian Journal of Mathematical Physics

, Volume 20, Issue 2, pp 129–137 | Cite as

Values of twisted Barnes zeta functions at negative integers

  • A. BayadEmail author
  • Y. Simsek
Article

Abstract

In this paper, we study analytical and arithmetical properties of the twisted zeta function \(\Gamma (s)^{ - 1} \int_0^\infty {e^{ - xt} t^{s - 1} } \prod\nolimits_{j = 1}^N {\frac{{a_j t - \log (w^a j)}} {{1 - w^{a_j } e^{a_j t} }}dt} \), where ℜ(s) > N, ℜ(x) > 0, w ∈ ℂ\{0}, N ∈ ℤ, and a 1, …, a N have positive real parts. These functions have many interesting properties. We prove a collection of fundamental identities satisfied by zeta functions of this kind. For instance, special values of these zeta functions are related to twisted Barnes numbers and polynomials. This gives us a new elementary approach to new and known results concerning the Barnes zeta functions. In particular, we derive some well-known results on the Hurwitz zeta functions.

Keywords

Zeta Function Negative Integer Positive Real Part Arithmetical Property Euler Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Département de mathématiquesUniversité d’Evry Val d’Essonne, Bâtiment I.B.G.B.I.Evry CedexFrance
  2. 2.Faculty of Arts and Science, Department of MathematicsUniversity of AkdenizAntalyaTurkey

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