| Budget Amount *help |
¥15,080,000 (Direct Cost: ¥11,600,000、Indirect Cost: ¥3,480,000)
Fiscal Year 2014: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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| Outline of Final Research Achievements |
Mainly concentrated on non-abelian zeta functions. Historic achievements are (1) introduce pure non-abelian zeta functions for function fields motivated by Driffield's work on counting super-cuspidal Galois representations, (2) prove jointly with Zagier the Riemann hypothesis for pure zetas of elliptic curves, (3) discover two levels of structures for distributions of zeta zeros. We explain (3) in details only. Unlike for distributions of Riemann zeros, the classical delta distributions are of Dirac type. In concrete terms, this means that the delta sequences of pair correlations have accumulating points. This is very different from that of Gaussian unitary ensembles (GUE). However, motivated by the work (2), we blow-up the infinitesimal neighborhood of these accumulating points to introduce totally new big Delta sequences and hence to discover the second level structure of the distributions of our zeta zeros. We conjecture that the structure of big Delta distributions are that of GUE.
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