| Project/Area Number |
23540034
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kinki University |
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Principal Investigator |
CHINEN Koji 近畿大学, 理工学部, 准教授 (30419486)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 数論 / ゼータ関数 / 剰余位数 / 原子根分布 / 自然密度 / 平方剰余 |
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| Research Abstract |
In this research, some results are obtained in the subject "distribution of the residual orders", in which the author has been involved. This is to investigate the distribution of D_a(p), where D_a(p) is the order of a mod p (a is an integer greater than 1, which is not a h-th power and p is a prime). More precisely, the problem of determining the natural density of p such that D_a(p) is congruent to l mod k. As generalizations of this problem, we obtained some results in the case where a quadratic resisue condition is added (Chinen-Tamura, 2012), and where mod pq instead of mod p (Murata-Chinen, 2013).
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