| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Research Abstract |
The aim of our study is to establish fundamental results on zeta functions for automorphic forms (automorphic L-functions) such as the analytic continuations and the functional equations, through their integral representations (zeta integrals). Using explicit formulas for generalized spherical functions, that is, special functions appearing in the Fourier expansions of automorphic forms, we have computed archimedean zeta integrals. Especially we calculate the archimedean zeta integrals for the L-functions on SO(2n+1)×GL(m) and the standard L-function on GL(3) and obtained the local and the global functional equations.
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