| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
A functional relation for the multiple polylogarithm which gives an analytic continuation of the multiple polylogarithm was obtained. We first showed the functional relation for the double polylogarithm by using a function which interpolates the harmonic numbers. After that, we give the functional relation for multiple polylogarithm by constructing a function which interpolates the multiple harmonic numbers and investigating residues of the interpolation equation. Furthermore, we try to evaluate multiple higher Mahler measures for several polynomials by using such functional relations. This research was a joint work with Kusunoki and Nakamura. Recurrence formula for poly-Bernoulli numbers was obtained. In fact, we showed similar recurrence formulas hold for the generalized poly-Bernoulli polynomials. Furthermore, we showed that the recurrence formula can be regarded as an enumeration formula for certain restricted lonesum matrices. This research was a joint work with Ohno.
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