2012 Fiscal Year Final Research Report
Unitary Jacobi forms and primitive theta functions
| Project/Area Number |
22540012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MURASE Atsushi 京都産業大学, 理学部, 教授 (40157772)
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| Project Period (FY) |
2010 – 2012
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| Keywords | ユニタリ群 / ヤコビ形式 / 保型L関数 / Hecke環 |
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| Research Abstract |
We determined the structure of Jacobi Hecke algebra whose index is a maximal even integral matrix and obtained zonal spherical functions corresponding to irreducible representations of the Hecke algebra, moreover, we showed a relation between a non-commutative Jacobi Hecke algebra and the group ring of a dihedral group (joint work with N. Hashizume). As a global problem, we gave a new system of generators for the ring of paramodular forms of degree 2 and level 2 or 3, by using theta lifts and Klingen Eisenstein series (joint work with Y. Iwahori).
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