| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
In this study, we obtained an explicit dimension formula for spaces of Siegel cusp forms of degree two with respect to paramodular groups of squarefree level, and also a relation between dimensions of spaces of different automorphic forms. As an applications, we proposed two conjectures. First, we proposed a conjecture on a correspondence which preserves L-functions. It is a generalization of a known conjecture for the cases of prime level. Second, we proposed a lifting conjecture for Siegel modular forms with respect to non-split symplectic groups from elliptic cusp forms. In addition, we carried out explicit calculations of L-functions in the case of discriminant 6 and gave numerical evidence of the above conjectures.
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