2012 Fiscal Year Final Research Report
Studies on automorphic forms and algebraic combinatorics connected via theta map
| Project/Area Number |
21740021
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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 |
Algebra
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| Research Institution | Kochi University |
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Principal Investigator |
OURA Manabu 高知大学, 教育研究部自然科学系, 准教授 (50343380)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 代数的組合せ論 / 保型形式 |
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| Research Abstract |
An E-polynomial is mapped to a modular form. We observed the obtained modular forms in genus 1. Originally E-polynomials are introduced as a counterpart of Eisenstein series and we found similar properties as Eisenstein series. The obtained modular forms have zeros on the circle of radius 1 in the fundamental region and those zeros have the so-called separation property. However, they are not proved and are expected to be clear in our subsequent research.
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