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A character on the quasi-symmetric functions coming from multiple zeta values. (English) Zbl 1163.05334
Summary: We define a homomorphism $$\zeta$$ from the algebra of quasi-symmetric functions to the reals which involves the Euler constant and multiple zeta values. Besides advancing the study of multiple zeta values, the homomorphism $$\zeta$$ appears in connection with two Hirzebruch genera of almost complex manifolds: the $$\Gamma$$-genus (related to mirror symmetry) and the $$\hat{\Gamma}$$-genus (related to an $$S^1$$-equivariant Euler class). We decompose $$\zeta$$ into its even and odd factors in the sense of Aguiar, Bergeron, and Sottille, and demonstrate the usefulness of this decomposition in computing $$\zeta$$ on the subalgebra of symmetric functions (which suffices for computations of the $$\Gamma$$- and $$\hat{\Gamma}$$-genera).

##### MSC:
 05E05 Symmetric functions and generalizations 11M32 Multiple Dirichlet series and zeta functions and multizeta values 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 57R20 Characteristic classes and numbers in differential topology
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