| 李伟平,王天泽.混合幂的素变数丢番图逼近[J].数学年刊A辑,2010,31(2):247~256 |
| 混合幂的素变数丢番图逼近 |
| Diophantine Approximation with Prime Variables and Mixed Powers |
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| DOI： |
| 中文关键词: 丢番图逼近 察变数 混合幂 Davenport-Heilbronn方法 |
| 英文关键词:Diophantine approximation Prime variables Mixed powers Davenport-Heilbronn method |
| 基金项目:国家自然科学基金 |
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| 中文摘要: |
| 证明了,如果λ1,λ2,λ3,λ4是正实数,λ1/λ2是无理数和代数效,V是well-spaced序列,δ>0,那么对于ν,∈V,ν≤X,ε>0,使得|λ1p21+λ2p22+λ3p33+λ4p34-ν|<ν-δ没有素数解P1,p2,p3,p4的ν的个数不超过O(X20/21+2δ+ε). |
| 英文摘要: |
| This paper shows that: Let λ1,λ2,λ3,λ4 be positive real numbers and suppose that λ1/λ2 is irrational and algebraic. Let V be a well-spaced sequence, δ > 0. Then, for any given ε> 0, the number of ν∈V with ν≤X for which|λ1p21+λ2p22+λ3p33+λ4p34-ν|<ν-δhas no solution in primes P1, P2, P3, P4 does not exceed O(X20/21+2δ+ε). |
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