Zeta values
Arborified multiple zeta values
... multiple zeta values first appears in 1981 in a preprint of Jean Ecalle under the name ”moule ζ • < ”, in the context of resurgence theory in complex analysis [13, Page 429], together with its companion ...
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Arithmetic of linear forms involving odd zeta values
... zeta values ζ(3), ζ(5), . . . ; in particular, he is able to prove [Ri1] that there are infinitely many irrational numbers in the set of the odd zeta values. A further generalization of the ...
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Well-poised hypergeometric service for diophantine problems of zeta values
... (due to F. J. W. Whipple and W. N. Bailey) for very-well-poised hypergeo- metric series. The aim of this paper is to demonstrate potentials of the well-poised hypergeometric service (series and integrals) in solving ...
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Renormalisation of q-Regularised Multiple Zeta Values
... multiple zeta values at negative ...different values to MZVs at negative arguments, while preserving the quasi-shuffle ...different values for MZVs at negative arguments, based on ...
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A sum-shuffle formula for zeta values in Tate algebras
... such zeta values satisfies a sum-shuffle product formula, and this will be again deduced from properties of twisted power sums (Theorem ...multiple zeta values in ...
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Arithmetic of values of L-functions and generalized multiple zeta values over number fields
... classical Zeta Values Classically, multiple Zeta values(MZVs) are the periods of mixed Tate motives, namely the MZVs are iterated integrals on P 1 ∖ ...
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Integral identities and constructions of approximations to zeta-values
... (Theorem 2) connected to the construction of functional linear forms in polylogarithmic functions In this way since we have the equality Lk(1) _ «(k) one can construct small linear forms in zeta-values at ...
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Unfolding the double shuffle structure of q-multiple zeta values
... Since terms of depth smaller than |v| + 1 disappear in the limit q → 1, identity (67) reduces to Hoffman’s regularization relations (18) for MZVs. As there are no regularization issues involved, no correction analogous ...
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Renormalisation group for multiple zeta values
... ζ p´aqζp´bq “ ζp´a, ´bq ` ζp´b, ´aq ` ζp´a ´ bq, obtained by imitating (3), it is natural to ask the question of how to extend MZVs beyond depth one to arguments in Z, such that the quasi-shuffle relations are preserved. ...
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Duality and (q-)multiple zeta values
... restrict this construction to non-negative arguments in the context of the quasi-shuffle product, then the coproduct of convergent words coincides with the coproduct obtained from the duality construction. As a result ...
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From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
... special values of infinite sums of single-valued multiple polylogarithms, and these infinite sums are proposed in the reference to be a single-valued analogue of elliptic multiple polylogarithms 2 ...multiple ...
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A new class of identities involving Cauchy numbers, harmonic numbers and zeta values
... modified zeta function of order k. The evaluation of the values of these functions F k at positive integers reveals a wide class of identities linking Cauchy numbers, harmonic numbers and zeta ...
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A note on certain alternating series involving zeta and multiple zeta values
... In this section, we consider a more general class of series of the previous type replacing zeta values with certain multiple zeta values. We prove our formula (3) and deduce some interesting ...
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Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
... Abstract. We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas ...
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Generating functions for multiple zeta star values
... multiple zeta values (MZVs) have been of in- terest for mathematicians and physicists for more than two ...ple zeta star values in general ...multiple zeta star values (MZSVs) ...
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Nested sums of symbols and renormalised multiple zeta functions
... multiple zeta values, which converge for Re(s 1 + · · · + s m ) > nm for any m ∈ {1, ...multiple zeta values with the supremum norm replaced by the Euclidean norm, the main difficulty ...
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Twisted characteristic $p$ zeta functions
... and zeta values, Annals of Mathematics 132 (1990), ...Multizeta values for F q [t], their period interpretation, and relations between them, International Mathematics Research Notices ...L-series ...
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Multiple zeta functions and polylogarithms over global function fields
... [15] K. Hessami Pilehrood, T. Hessami Pilehrood & J. Zhao, “On q-analogs of some fami- lies of multiple harmonic sums and multiple zeta star value identities”, Commun. Number Theory Phys. 10 (2016), no. 4, p. ...
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Irrationalité de $\zeta (s)$ pour $s \le q$ dans certains modules de Drinfeld de rang $1$
... [1] L. CARLITZ, On certain functions connected with polynomials in a Galois field, Duke Math. J. 1 (1935), 137-168. [2] H. CHÉRIF et B. de MATHAN, Irrationality measures of Carlitz zeta values in positive ...
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Inverse binomial series and values of Arakawa-Kaneko zeta functions
... special values at positive integers of two classes of zeta functions of Arakawa-Kaneko-type by means of certain inverse binomial series involving harmonic sums which appeared fifteen years ago in physics in ...
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