2010 Fiscal Year Final Research Report
Analysis of stochastic processes on the adeles
| Project/Area Number |
19740055
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
YASUDA Kumi Keio University, 商学部, 准教授 (40284484)
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| Project Period (FY) |
2007 – 2010
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| Keywords | アデール環 / 確率解析 |
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| Research Abstract |
Construction of Markov processes on the adeles, and analysis of the distribution of the exit time from the p-adic integer ring, and the p-adic norm of the p-component of the processes at the exit time. Description of the distribution of the exit time of the adelic processes from the finite integral adeles. Formulae for Riemann's zeta and other functions with Euler product representations in terms of the exit time of the processes and the p-adic norm of the p-component at the exit time. Functional equations relating the values of Riemann's zeta function at a point and its complex conjugates or its real part.
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