In this paper, we study specific families of multiple zeta values which closely relate to the linear part of Kawashima's relation. We obtain an explicit basis of these families, and investigate their interpolations to complex functions. As a corollary of our main results, we also see that the duality formula and the derivation relation are deduced from the linear part of Kawashima's relation.2010 Mathematics Subject Classification. Primary 11M32.
We investigate linear relations among a class of iterated integrals on the Riemann sphere minus four points 0, 1, z and ∞. Generalization of the duality formula and the sum formula for multiple zeta values to the iterated integrals are given.
In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple harmonic sums. We also conjecture several weighted sum formulas of similar flavor for finite multiple zeta values.
In this paper, we prove certain algebraic identities, which correspond to differentiation of the shuffle relation, the stuffle relation, and the relations which arise from Möbius transformations of iterated integrals. These formulas provide fundamental and useful tools in the study of iterated integrals on a punctured projective line. e a A {0,1,z} e b ,
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