2012 Fiscal Year Final Research Report
Problems on geometric asymptotic analysis over convex polytopes
| Project/Area Number |
21740117
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
TATE Tatsuya 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00317299)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 幾何学的漸近解析 / 凸多面体 / リーマン和 / トーリック多様体 / ランダム行列理論 / 量子ウォーク / エータ関数 |
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| Research Abstract |
A convex polytope is said to be a lattice polytope if each vertex is a lattice point. An asymptotic expansion formula for the Riemann sums of general smooth functions over lattice polytopes was obtained. This formula is regarded as a generalization of the so-called local Euler-Maclaurin formula due to Berline-Vergne. Furthermore, an explicit formula for the third term in the expansion was obtained in case where the polytope is Delzant.
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