On Barnes' Multiple Zeta and Gamma Functions

By S. Ruijsenaars. 2000

177 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/846caff2552c4a6ea027cf45f8ee0a80e1075883

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In Algebra and Number Theory

1. V. Spiridonov
2. A. Okounkov
3. D. Martelli
4. D. Cassani
5. Davesh Maulik
6. Benjamin Assel
7. K. Tohge
8. R. Halburd

In Applied Mathematics

1. R. Korhonen
2. R. Halburd
3. K. Tohge
4. A. Okounkov
5. Davesh Maulik
6. V. Spiridonov
7. Eduardo Friedman
8. Z. Komargodski

Citations in the corpus

• Holomorphic curves with shift-invariant hyperplane preimages (2009, methodology): “This research was supported in part by the Academy of Finland Grant #112453, #118314 and #210245, a grant from the EPSRC, the Isaac Newton Institute for Mathematical Sciences, the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (C) #19540173, #22540181, and a project…”
• The modular properties and the integral representations of the multiple elliptic gamma functions (2003, unknown): “Our main purpose of this paper is to derive the modular properties of the multiple elliptic gamma functions Gr(z|τ0, · · · , τr) with the multiple sine functions Sr(z|ω1, · · · , ωr) and the multiple Bernoulli polynomials Br,n(z|ω1, · · · , ωr).”
• Essays on the theory of elliptic hypergeometric functions (2008, background): “Because of the grown interest the Barnes theory was sufficiently widely discussed in the recent literature, for instance, in [19, 26, 27, 28, 37].”
• Quantum Groups and Quantum Cohomology (2012, methodology): “or any K-theory class Lwhose Chern character is defined. Here ln(−1) u= u(lnu−1) etc. This generalizes (6.8) and is the usual ζ-regularization of infinite products given by Γ-functions, see for example [96, 105]. 132 133 6.1 The core Yangian In particular, this defines e(Nb −) e(Nb − ⊗~) for Nb − = − ”
• Defects and quantum Seiberg-Witten geometry (2014, unknown): “Barnes’ gamma functions are defined as regularized infinite products [95, 96] ΓN (z|w1, · · · , wN ) = exp (∂sζN (s, z;w1, · · · , wN )|s=0) ∼ ∏ n1,··· ,nN≥0 (z + n · w)−1 , (C.”
• Unitary Representations of Uq(??}(2,ℝ)),¶the Modular Double and the Multiparticle q-Deformed¶Toda Chain (2001, background): “See also relevant items on the subject in [39,40].”
• Shintani–Barnes zeta and gamma functions (2004, background): “[11]), and in Section 2 we generalize it to zN;n: The principal result of Section 2 is that zN;nðs;wÞ=pN;nðsÞ extends to a function that is entire in s and analytic in the wj and aij in the domains Dn :1⁄4 fwACjReðwjÞ40; 1pjpng; ð1:12Þ and DN;n :1⁄4 faijACjReðaijÞ40; 1pipN; 1pjpng: ð1:13Þ The associ”
• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function (2008, unknown): “4 Barnes double gamma function Concerning the notation of the double gamma function we follow Ruijsenaars, [10].”
• The Casimir energy in curved space and its supersymmetric counterpart (2015, background): “One-loop determinant regularizations are based on the use of multiple gamma functions [52] and generalized zeta functions.”