Derivation and double shuffle relations for multiple zeta values

By K. Ihara. Compositio Mathematica, 2006

433 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/f2f97131e8231fcd2e532d6156c27fa69905dbea

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Citations in the corpus

An odd variant of multiple zeta values (2016, background): “Both the duality theorem and the “double shuffle relations” [17] of multiple zeta values are missing for multiple t-values.”
A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS (2017, background): “of solutions to linearized double-shuffle equations in polynomials (that is, with no poles) is related to the structure of depth-graded motivic multiple zeta values [3, 24].”
Euler's constant: Euler's work and modern developments (2013, background): “In addition the values (Γ(pq )) q where pq is a positive rational number are periods, see Kontsevich and Zagier [186, p. 775], André [9, Chap.”
The Multiple Zeta Value data mine (2009, background): “(c) All relations between MZVs are given by the extended double-shuffle relations [79], cf.”
Depth-graded motivic multiple zeta values (2013, methodology): “Following [21], consider the relation”
Double Zeta values and modular forms (2006, background): “Double zeta values are a special case of multiple zeta values, dened by sums like (1) but with longer decreasing sequences of integers, which are known to satisfy a collection of relations called the double shue relations (cf., e.g., [ 3 ], [5], [12]).”
Renormalization of multiple zeta values (2006, methodology): “Let ~s = (s1, · · · , sk) with positive integers s1, · · · , sk and Z ∗ ~s (T ) be the regularized MZVs of Ihara-Kaneko-Zagier.”
Double shuffle relation for associators (2008, neutral): “There are several formulations of the relations (see [ IKZ , R]).”
Standard relations of multiple polylogarithm values at roots of unity (2007, background): “However, when the level N ≥ 3, these relations are not complete in general, as we shall see in this paper.”
A class of non-holomorphic modular forms I (2017, background): “This paper is based on a talk at a conference in honour of Don Zagier’s birthday, and connects with his work in several ways: through his work on modular graph functions [10], on single-valued polylogarithms [33], on period polynomials [22], on periods [21], on multiple zeta values [15], on double E”
Feynman integrals and hyperlogarithms (2015, background): “For the proof we need the well-known parity theorem on multiple zeta values [104, 172].”
On the algebra of quasi-shuffles (2005, neutral): “Observe that this product is not a graded product, but only a filtered product, since a⊗ b + b⊗ a ∈ R⊗2 and a · b ∈ R.”