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# Functional Equations and the Harmonic Relations for Multiple Zeta Values

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 Title: Functional Equations and the Harmonic Relations for Multiple Zeta Values Authors: Machide, Tomoya Browse this author Keywords: multiple zeta values Issue Date: 2006 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 765 Start Page: 1 End Page: 11 Abstract: Let $\theta (x)$ denote Jacobi's theta function. We show that the function $F_\xi (x) = (\theta '(0) \theta (x+\xi) )/ (\theta (x) \theta (\xi))$ satisfies functional equations, which is a generalization of the harmonic relations for multiple zeta values. Type: bulletin (article) URI: http://hdl.handle.net/2115/69573 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics