Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1038.11058
Kim, Taekyun
On Euler-Barnes multiple zeta functions. (English)
[J] Russ. J. Math. Phys. 10, No. 3, 261-267 (2003). ISSN 1061-9208; ISSN 1555-6638/e

Summary: We define the analytic continuation of multiple zeta functions (the Euler-Barnes multiple zeta functions) depending on parameters $a_1,a_2,\dots,a_r$ taking positive values in the complex number field, $$\zeta_r(s,w,u\mid a_1,\dots,a_r)=\sum^\infty_{m_1,\dots,m_r=0}\ \frac{u^{-(m_1+\cdots+m_r)}}{(w+m_1a_1+\cdots+m_ra_r)^s}\,,$$ where $\Re w > 0$ and $u\in \bbfC$ with $\vert u\vert > 1$. We also study some interesting properties of the Euler-Barnes multiple zeta functions at negative integers. In the final section, we construct $p$-adic Euler integrals used in the proof of Witt-type formulas for the Barnes-type multiple Frobenius-Euler numbers.

MSC 2000:: *11M41 Other Dirichlet series and zeta functions

Cited in: Zbl 1100.11010 Zbl 1085.11009 Zbl 1060.11010

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]