| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
We mainly studied multiple zeta functions defined by Arakawa--Kaneko and Kaneko--Tsumura, and their values at both positive and negative integral points, namely multiple zeta and zeta-star values and multi-poly-Bernoulli numbers. In particular, we defined t-interpolation of Arakawa--Kaneko and Kaneko--Tsumura multiple zeta functions and gave its special values at positive integral points in terms of t-multiple zeta values, and also gave its values at negative integral points in terms of Landen type interpolated multi-poly-Bernoulli polynomials. Moreover as a joint work with Sasaki, we obtain a kind of recursion relation of multi-poly-Bernoulli numbers. As a joint work with Kawasaki, we found a type of generating algorithm of multi-poly-Bernoulli polynomials, and newly pointed out a basic connection of them to truncated multiple zeta values. Moreover we studied many topics including the usage of relations among two-colored ordered graphs and multiple zeta values.
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