| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
In this period, we have studied the spherical functions on the space of unitary hermitain forms with even residual characteristic and on the space of quaternion hermitian forms with odd residual characteristic, as interesting $p$-adic homogeneous spaces from the perspective of Number Theory. For both cases, we have constructed the typical spherical functions from relative invariants, and given those functional equations with respect to the Weyl groups, then obtained the explicit formulas by using our previous result on general expression formulas of spherical functions. In the main terms of the spherical functions there appear a series of Weyl-invariant polynomials and play an important role for the harmonic analysis on the spaces through the spherical transform.
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