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On Multiple zeta values and their q-analogues

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On Multiple zeta values and their q-analogues
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Hopf-Algebraic Renormalization of Multiple Zeta Values and their q-analogues
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15
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
After a brief introductory account, I’ll explain how a quasi-shuffle compatible definition (by no means unique) of multiple zeta values can be given for integer arguments of any sign, through Connes-Kreimer’s Hopf-algebraic renormalization. Finally, I’ll introduce the Ohno-Okuda-Zudilin model of q-analogues for multiple zeta values, describe the algebraic structure which governs it, and explain how it could open a way to the more delicate renormalization of shuffle relations.