混合幂次为2和3的整数变量非线性型的整数部分

李伟平, 赵峰, 王天泽

数学学报 ›› 2012, Vol. 55 ›› Issue (4) : 727-736.

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数学学报 ›› 2012, Vol. 55 ›› Issue (4) : 727-736. DOI: 10.12386/A2012sxxb0070
论文

混合幂次为2和3的整数变量非线性型的整数部分

    李伟平1, 赵峰2, 王天泽2
作者信息 +

The Integer Parts of Nonlinear Form with Integer Variables and Mixed Powers 2 and 3

    Wei Ping LI1, Feng ZHAO2, Tian Ze WANG2
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文章历史 +

摘要

证明了:假设λ1,...,λ6是正实数,λ12是无理数, Dirichlet L 函数满足黎曼猜想, x1,…,x6是正整数,那么,λ1x122x223x334x435x536x63的整数部分可表示无穷多素数.

Abstract

The present paper proved that if λ1,...,λ6 are positive real numbers, λ12 is irrational, all Dirichlet L-functions satisfy the Riemann Hypothesis, then, the integer parts of λ1x122x223x334x435x536x63are infinitely many primes for natural numbers x1,…,x6.

关键词

整数变量 / 丢番图逼近 / Davenport--Heilbronn方法

Key words

integer variables / diophantine approximation / Davenport-Heilbronn method

引用本文

导出引用
李伟平, 赵峰, 王天泽. 混合幂次为2和3的整数变量非线性型的整数部分. 数学学报, 2012, 55(4): 727-736 https://doi.org/10.12386/A2012sxxb0070
Wei Ping LI, Feng ZHAO, Tian Ze WANG. The Integer Parts of Nonlinear Form with Integer Variables and Mixed Powers 2 and 3. Acta Mathematica Sinica, Chinese Series, 2012, 55(4): 727-736 https://doi.org/10.12386/A2012sxxb0070

参考文献

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基金

国家自然科学基金资助项目(11071070);河南省教育厅自然科学研究计划(2011B110002)
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