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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Euler reflexion formulas for motivic multiple zeta functions

Authors: Lê Quy Thuong and Nguyen Hong Duc
Journal: J. Algebraic Geom. 27 (2018), 91-120
Published electronically: February 17, 2017
MathSciNet review: 3722691
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Abstract | References | Additional Information


We introduce a new notion of $\boxast$-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability of and commuting with the limit of rational series. In the same context, we define a motivic multiple zeta function with respect to an ordered family of regular functions, which is integrable and connects closely to Denef-Loeser’s motivic zeta functions. We also show that the $\boxast$-product is associative in the class of motivic multiple zeta functions.

Furthermore, a version of the Euler reflexion formula for motivic zeta functions is nicely formulated to deal with the $\boxast$-product and motivic multiple zeta functions, and it is proved for both univariate and multivariate cases by using the theory of arc spaces. As an application, taking the limit for the motivic Euler reflexion formula we recover the well-known motivic Thom-Sebastiani theorem.

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Additional Information

Lê Quy Thuong
Affiliation: Department of Mathematics, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan District, Hanoi, Vietnam

Nguyen Hong Duc
Affiliation: Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi City, Quang Binh, Vietnam
Address at time of publication: BCAM – Basque Center for Applied Mathematics, Mazarredo, 14, 48009 Bilbao, Basque Country, Spain
MR Author ID: 842994

Received by editor(s): November 25, 2015
Received by editor(s) in revised form: May 2, 2016
Published electronically: February 17, 2017
Additional Notes: The first author’s research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant No. FWO.101.2015.02. The second author was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant No. 101.04-2014.23. This research was also supported by ERCEA Consolidator Grant 615655 - NMST and by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
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