On Witten multiple zeta-functions associated with semisimple Lie algebras. II.

DOI10.2969/jmsj/06220355zbMath1210.11099arXiv1302.4285OpenAlexW3101078787MaRDI QIDQ978492

Yasushi Komori, Hirofumi Tsumura, Kohji Matsumoto

Publication date: 24 June 2010

Published in: Journal of the Mathematical Society of Japan, Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.4285

zbMATH Keywords

Lie algebrasroot systemsBernoulli polynomialssemi-simple Lie algebraWitten zeta-functionsWitten multiple zeta-functionpositive integer points

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Other Dirichlet series and zeta functions (11M41) Simple, semisimple, reductive (super)algebras (17B20) Multiple sequences and series (40B05) Multiple Dirichlet series and zeta functions and multizeta values (11M32) Root systems (17B22)

Related Items (25)

ON <i>q</i>-ANALOGUES OF ZETA FUNCTIONS OF ROOT SYSTEMS ⋮ On complex zeros off the critical line for non-monomial polynomial of zeta-functions ⋮ Zeta-functions of root systems and Poincaré polynomials of Weyl groups ⋮ Cyclic relation for multiple zeta functions ⋮ Renormalised conical zeta values ⋮ Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems ⋮ Certain convolution formulas for multiple series ⋮ An overview and supplements to the theory of functional relations for zeta-functions of root systems ⋮ A study on multiple zeta values from the viewpoint of zeta-functions of root systems ⋮ Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces ⋮ An interpolation of Ohno's relation to complex functions ⋮ ALTERNATING EULER SUMS AND SPECIAL VALUES OF THE WITTEN MULTIPLE ZETA FUNCTION ATTACHED TO ⋮ Functional equation for the Mordell-Tornheim multiple zeta-function ⋮ Evaluation of Tornheim's type of double series ⋮ Zeta and \(L\)-functions and Bernoulli polynomials of root systems ⋮ On Witten multiple zeta-functions associated with semisimple Lie algebras. II. ⋮ Witten multiple zeta values attached to \(\mathfrak {sl}(4)\) ⋮ Multiple zeta values and zeta-functions of root systems ⋮ Computation and Experimental Evaluation of Mordell–Tornheim–Witten Sum Derivatives ⋮ ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV ⋮ Double Lerch value relations and functional relations for Witten zeta functions ⋮ An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers ⋮ Zeta functions associated to admissible representations of compact 𝑝-adic Lie groups ⋮ A conical approach to Laurent expansions for multivariate meromorphic germs with linear poles ⋮ ON A CERTAIN CONVOLUTION OF POLYLOGARITHMS

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