| Budget Amount *help |
¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2019: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2018: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2017: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Outline of Final Research Achievements |
First, we introduce and study zeta functions for number fields associated to reductive groups and their maximal parabolic subgroups and establish their the Riemann hypothesis for Chevelley groups. Then we develop a special zeta uniformity theory for rank n non-abelian zeta functions and SLn zeta functions for both number fields, and function fields (with D. Zagier). As a by-product, with my formal phD student, K. Sugahara, we develop a new number theoretic adelic cohomology theory for arithmetic varieties using ind-pro topology, and as an application, we establish a new type of reciprocity laws for arithmetic surfaces and show that the first arithmetic adelic cohomology group for arithmetic surfaces are indeed finite, which offer a new type of intrinsic invariants for these surfaces. Among others, one big volume on 'Zeta functions of reductive groups and their zeros' of mine is published by the World Scientific and two joint papers with Zagier are published by the leading journal PNAS.
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