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18 results on '"Okuda, Jun-ichi"'

1. On relations for the $q$-multiple zeta values

Author

Okuda, Jun-ichi and Takeyama, Yoshihiro

Subjects
Mathematics - Quantum Algebra, Mathematics - Number Theory, 05A30, 11B65, 33D15
Abstract

We prove some relations for the $q$-multiple zeta values ($q$MZV). They are $q$-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the dimension of the space spanned by $q$MZV's over $\Q$, and present an application to MZV., Comment: 16 pages

Published
2004

2. The Sum Formula of Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation

Author

Okuda, Jun-ichi and Ueno, Kimio

Subjects
Mathematics - Number Theory, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, 11M06, 40B05
Abstract

The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered in the framework of the theory of the formal Knizhnik-Zamolodchikov equation., Comment: 26 pages, 4 figures, with the appendix by Michitomo Nishizawa and the second author

Published
2003

3. Duality formulas of the Special Values of Multiple Polylogarithms

Author

Okuda, Jun-ichi

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 40B05, 33E20
Abstract

The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the viewpoint of a connection matrix of Fuchsian equations, we derive two kinds of duality of these values., Comment: 18 pages (in 12pt)

Published
2003

4. Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms

Author

Okuda, Jun-ichi and Ueno, Kimio

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Classical Analysis and ODEs, 11M06, 40B05
Abstract

The relationship between the Ohno relation and multiple polylogarithms are discussed. Using this relationship, the algebraic reduction of the Ohno relation is given., Comment: 28 pages

Published
2003

5. New Approach to Ohno Relation for Multiple Zeta Values

Author

Okuda, Jun-ichi and Ueno, Kimio

Subjects
Mathematics - Number Theory, 11M06, 40B05
Abstract

Ohno's relation gives a large family of relations of the multiple zeta values. We shall show functional relations of generating functions of Ohno's relation. With these relations we present a new proof of Ohno's relation., Comment: 15 pages

Published
2001

12. The Sum Formula for Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation

Author

Okuda Jun-ichi and Ueno Kimio

Subjects
Mellin transform, Pure mathematics, Mathematics::Classical Analysis and ODEs, TheoryofComputation_GENERAL, Linear fractional transformation, Connection (mathematics), Riemann zeta function, Algebra, High Energy Physics::Theory, symbols.namesake, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, Mathematics::Quantum Algebra, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, symbols, Euler's formula, Mellin inversion theorem, Computer Science::Symbolic Computation, Perron's formula, MathematicsofComputing_DISCRETEMATHEMATICS, Mathematics
Abstract

The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered in the framework of the theory of the formal Knizhnik-Zamolodchikov equation.

Published
2008

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