PDF(443 KB)
PDF(443 KB)
PDF(443 KB)
素变量混合幂丢番图逼近
Diophantine Approximation with Prime Variables and Mixed Powers
设λ1，λ2，λ3，λ4为不全为负的非零实数，λ1/λ2是无理数和代数数.V是具有良好间隔的序列，δ>0.本文证明了：对于任意ε>0及v∈V，v≤X，使得不等式|λ1p12+λ2p22+λ3p33+λ4p43-v|<v-δ无素数解p1，p2，p3，p4的v的个数不超过O（X7/8+2δ+ε）.这改进了之前的结果.
Let λ1, λ2, λ3, λ4 be non-zero real numbers, not all negative, and let λ1/λ2 be irrational and algebraic. Let V be a well-spaced sequence and δ > 0. We prove that for any given ε > 0, the number of v satisfying v ∈ V and v ≤ X for which|λ1p12+λ2p22+λ3p33+λ4p43-v|<v-δ has no solution in primes p1, p2, p3, p4 does not exceed O(X7/8+2δ+ε). This gives an improvement of an earlier result.
丢番图不等式 / 素数 / Davenport-Heilbronn方法 {{custom_keyword}} /
diophantine inequalities / prime / Davenport-Heilbronn method {{custom_keyword}} /
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国家自然科学基金资助项目（11371122，11471112）；河南省科技创新杰出人才计划（134200510017）；河南财经政法大学2016年青年拔尖人才
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