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UNFOLDING THE DOUBLE SHUFFLE STRUCTURE OF $q$-MULTIPLE ZETA VALUES

Part of: Arithmetic algebraic geometry Zeta and $L$-functions: analytic theory Basic hypergeometric functions

Published online by Cambridge University Press:  24 April 2015

JAIME CASTILLO-MEDINA ,
KURUSCH EBRAHIMI-FARD  and
DOMINIQUE MANCHON
JAIME CASTILLO-MEDINA
Affiliation:
Universidad de València, Facultat de Ciències Matemàtiques, C/-Doctor Moliner, 50, 46100 Burjassot-Valencia, Spain email jaicasme@alumni.uv.es
KURUSCH EBRAHIMI-FARD
Affiliation:
Instituto de Ciencias Matemáticas, C/-Nicolás Cabrera, no. 13–15, 28049 Madrid, Spain email kurusch@icmat.es, kurusch.ebrahimi-fard@uha.fr
DOMINIQUE MANCHON*
Affiliation:
Université Blaise Pascal, CNRS–UMR 6620, 63177 Aubière, France email manchon@math.univ-bpclermont.fr
*
✉manchon@math.univ-bpclermont.fr
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Abstract

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We exhibit the double $q$-shuffle structure for the $q$MZVs introduced by Ohno et al. [‘Cyclic $q$-MZSV sum’, J. Number Theory132 (2012), 144–155].

Keywords

multiple zeta valuesbasic hypergeometric functionsq-analogueshuffle relationdouble shuffle

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 11G55: Polylogarithms and relations with $K$-theory 33D70: Other basic hypergeometric functions and integrals in several variables

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 368 - 388
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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