Finite and symmetric Mordell–Tornheim multiple zeta values
نویسندگان
چکیده
We introduce finite and symmetric Mordell–Tornheim type of multiple zeta values give a new approach to the Kaneko–Zagier conjecture stating that satisfy same relations.
منابع مشابه
Quasi-symmetric functions, multiple zeta values, and rooted trees
The algebra Sym of symmetric functions is a proper subalgebra of QSym: for example, M11 and M12 +M21 are symmetric, but M12 is not. As an algebra, QSym is generated by those monomial symmetric functions corresponding to Lyndon words in the positive integers [11, 6]. The subalgebra of QSym ⊂ QSym generated by all Lyndon words other than M1 has the vector space basis consisting of all monomial sy...
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for any collection of positive integers s1, s2, . . . , sl. By definition, Lis(1) = ζ(s), s ∈ Z, s1 ≥ 2, s2 ≥ 1, . . . , sl ≥ 1. (4.2) Taking, as before for multiple zeta values, Lixs(z) := Lis(z), Li1(z) := 1, (4.3) let us extend action of the map Li : w 7→ Liw(z) by linearity on the graded algebra H (not H, since multi-indices are coded by words in H). Lemma 4.1. Let w ∈ H be an arbitrary non...
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It is now a good time to go back to the MZV story. where F (a, b; c; z) denotes the hypergeometric function and i = √ −1. Proof. Routine verification (with a help of Lemma 4.1 for the left-hand side) shows that the both sides of the required equality are annihilated by action of the differential operator (1 − z) d dz 2 z d dz 2 − t 4 ; in addition, the first terms in z-expansions of the both si...
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ژورنال
عنوان ژورنال: Journal of The Mathematical Society of Japan
سال: 2021
ISSN: ['1881-1167', '0025-5645']
DOI: https://doi.org/10.2969/jmsj/84348434