2010 Fiscal Year Final Research Report
Research on additive problems concerning powers of primes.
| Project/Area Number |
20540002
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Iwate University |
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Principal Investigator |
KAWADA Koichi Iwate University, 教育学部, 准教授 (70271830)
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| Co-Investigator(Kenkyū-buntansha) |
OSHIKIRI Genーichi 岩手大学, 教育学部, 教授 (70133931)
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| Project Period (FY) |
2008 – 2010
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| Keywords | Waring問題 / Waring-Goldbach問題 / 素数 / べき乗数 / 加法的問題 |
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| Research Abstract |
We discovered that under certain circumstances, Davenport's diminishing range method has significant effects on the application of Wooley's method which provides sharp estimates for exceptional sets associated with additive problems. This method may be applied to various kinds of additive problems, and amongst others, we established new estimates for exceptional sets associated with sums of cubes, or biquadrates, of prime numbers. Also, we showed that every sufficiently large integer can be written as the sums of eight cubes of natural numbers that has at most two prime factors.
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