| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Research Abstract |
The paper entitled by ”KZ equation on the moduli space M_{0,5} and the harmonic product of multiple polylogarithms” appeared in Proc. London. Math. Soc.. In this article, we established the algebraic foundation such as the reduced bar algebra, and the geometric foundation such as the fiber space structure of the moduli space M_{0,5}, and showed the decomposition theorem of the fundamental solution of the KZ equation on M_{0.5}. Moreover we showed that the decomposition theorem is equivalent to the generalized harmonic product relations, and that they involve all the harmonic products of multiple polylogarithms of one variable. The paper entitled by ‘’The Inversion Formula of Polylogarithms abd the Riemann-Hilbert Problem” also was published last year. In this paper, we succeeded in characterzing polylogarithms by using the Riemann-Hilbert problem under a certain asymptotic condition.
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