| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We study zeta regularized products and the associated special functions, especially their algebraic and analytic properties. For example, we explicitly calculate "higher depth regularized products", which are generalizations of the usual regularized products, of the eigenvalues of the Laplacian on some manifolds. Moreover, we also investigate Ramanujan graphs in association with Ihara zeta functions, which are graph analogues of the zeta regularized products. Since Ramanujan graphs have very strong connectivity properties, it is easily expected that the graph remains to be Ramanujan even if one removes some edges from the complete graph. We can then clarify that the determination of the number of such removable edges are related to some problems on analytic number theory such as the conjecture of Hardy-Littlewood and Bateman-Horn.
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