Unitary Jacobi forms and primitive theta functions

Research Project

Project/Area Number	22540012
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Kanazawa University
Principal Investigator	SUGANO Takashi 金沢大学, 数物科学系, 教授 (30183841)
Co-Investigator(Renkei-kenkyūsha)	MURASE Atsushi 京都産業大学, 理学部, 教授 (40157772)
Project Period (FY)	2010 – 2012
Project Status	Completed (Fiscal Year 2012)
Budget Amount *help	¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000) Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000) Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000) Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords	ユニタリ群 / ヤコビ形式 / 保型L関数 / Hecke環 / 保型Ｌ関数
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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(4 results)