| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Research Abstract |
We introduced" higher depth zeta regularized products" as generalizations of the usual regularized products and have studied their analytic and algebraic properties. In particular, we have obtained explicit expressions of" higher depth determinants" of the Laplacian on some manifolds. Moreover, we also introduced" Schur multiple zeta functions" as extensions of the Euler-Zagier multiple zeta functions. Several fundamental properties and combinatorial formulas for the zeta functions have been obtained or expected.
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