Study on arithmetic invariants attached to automorphic forms
| Project/Area Number |
18540057
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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 | Kyoto Sangyo University |
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Principal Investigator |
MURASE Atsushi Kyoto Sangyo University, Faculty of Science, Professor (40157772)
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| Co-Investigator(Kenkyū-buntansha) |
SUGANO Takashi Kanazawa Unviersity, Institute of Natural Science, Professor (30183841)
YAMAGAMI Atsushi Kyoto Sangyo University, Faculty of Science, Associate Professor (00440876)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,910,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥510,000)
Fiscal Year 2007: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2006: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | automorphic form / Fourier coefficients / automorphic L-function / theta lift / period / algebraic group |
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| Research Abstract |
(1) For an elliptic cusp form f on a Hecke congruence subgroup and a Hecke character W of an imaginary quadratic field K, I showed that the square of a xertain CM-period attached to (f,W) is expressed in terms of the central value of the L-function attached to (f,W), when the level off is square free.
(2) We proposed a conjecture concerning a relation between the Fourier-Jacobi coefficients of a cusp form F on U(2,1) and the central values of automorphic L-functions attaced to F. The conjecture are proved when F is a holomorphic Eisenstein series or a unitary Kudla lift. The results in (1) are essentially used in the proof of the latter result. This is a joint work with Takashi Sugano.
(3) Let f and f' be automorphic forms on GL(2) and the multiplicative group of a quaternion algebra B, respectively. Let L(f,f') be the theta lift on Sp(1,1) constructed from (f,f'). We showed that L(f,f') is a Hecke eigenform if so are f and f'. We also showed that the Fourier coefficients of L(f,f') are expressed in terms of CM-periods of f and f'. This is a joint work with Hiro-aki Narita.
(4) A p-adic infinite family of Hilbert modular forms parameterized by an Affinoid Hecke variety is constructed. When the degree of the base field F is even, a p-adically analytic infinite family of Hilbert Hecke eigenforms of a fixed finite slope parameterized by weights is constructed. This is a work of Atsushi Yamagami.
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Report
(3 results)
Research Products
(13 results)
