q-Analogues of Multiple Zeta Values and Their Application in Renormalization

Singer J (2020)


Publication Type: Conference contribution

Publication year: 2020

Publisher: Springer

Book Volume: 314

Pages Range: 293-325

Conference Proceedings Title: Springer Proceedings in Mathematics and Statistics

Event location: Madrid ES

ISBN: 9783030370305

DOI: 10.1007/978-3-030-37031-2_11

Abstract

In this paper we report on recent developments on q-analogues of multiple zeta values (MZVs), which are power series in a formal parameter q that reduce to classical MZVs in the limit. First of all, we systematically develop the double shuffle relations of three q-models, whose shuffle products rely on a description of iterated Rota–Baxter operators. In the second part we use two of these q-models to construct solutions to the renormalization problem of MZVs, i.e., a systematic extension of MZVs to negative integers. In one case the renormalized MZVs satisfy the quasi-shuffle relations and in the other case the shuffle relations are verified.

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How to cite

APA:

Singer, J. (2020). q-Analogues of Multiple Zeta Values and Their Application in Renormalization. In José Ignacio Burgos Gil, Kurusch Ebrahimi-Fard, Herbert Gangl (Eds.), Springer Proceedings in Mathematics and Statistics (pp. 293-325). Madrid, ES: Springer.

MLA:

Singer, Johannes. "q-Analogues of Multiple Zeta Values and Their Application in Renormalization." Proceedings of the Workshop Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory, ICMAT-MZV 2014, Madrid Ed. José Ignacio Burgos Gil, Kurusch Ebrahimi-Fard, Herbert Gangl, Springer, 2020. 293-325.

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