Shintani–Barnes zeta and gamma functions

By Eduardo Friedman, S. Ruijsenaars. 2004

71 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/1b96f3d437403de5d13adbc2a1f5d750f7afd35f

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, background): “the n6= 0 constraint, but at present it is not clear to us at a technical level how exactly this would work out. We follow the conventions and denitions of multiple gamma and zeta functions given in [90]. The RHS of (D.1) can be written as Z+ = Y1 n 0;n 1;n 2 =0 ˆu ir’+2i’ 2ˇ + n 0 + i! 1n 1+i! 2n 2”
Defects and quantum Seiberg-Witten geometry (2014, background): “Barnes’ gamma functions are defined as regularized infinite products [97, 98]”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “Both elliptic gamma functions are directly related to the Barnes multiple gamma function of the third order [31, 83].”
Localization on Hopf surfaces (2014, methodology): “A natural regularization is to use the Barnes multiple zeta/gamma functions and we refer the reader to [52, 53] for definitions, notations and useful formulae, in particular for the function Γ3 and ζ3.”
$q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series (2005, background): “Friedm an and Ruijsenaars[9]showed thatShintani’swork on m ultiple zeta and gam m a functionscan be sim pli ed and extended by exploiting di erence equations.”
Essays on the theory of elliptic hypergeometric functions (2008, background): “The exact form of such a relation is (see, for instance, [26]) θ(e; p) = e2,2 Γ2(u; 1, τ)Γ2(1 + τ − u; 1, τ)Γ2(u − τ ; 1,−τ)Γ2(1 − u; 1,−τ) , (2.”