201 citations · 2.4k across the 113 of their papers we have counts for
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Evaluating Generating Functions for Periodic Multiple Polylogarithms
Kurusch Ebrahimi-Fard, W. Steven Gray, Dominique Manchon
The goal of the paper is to give a systematic way to numerically evaluate the generating function of a periodic multiple polylogarithm using a Chen-Fliess series with a rational ge…
Duality and (q-)multiple zeta values
Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer
Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zet…
Renormalisation group for multiple zeta values
Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer +1
Calculating multiple zeta values at arguments of any sign in a way that is compatible with both the quasi-shuffle product as well as meromorphic continuation, is commonly referred…
Transfer group for renormalized multiple zeta values
Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer +1
We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify th…
Renormalisation of q-regularised multiple zeta values
Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer
We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negativ…
The Hopf algebra of (q)multiple polylogarithms with non-positive arguments
Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer
We consider multiple polylogarithms in a single variable at non-positive integers. Defining a connected graded Hopf algebra, we apply Connes' and Kreimer's algebraic Birkhoff decom…