THE 'LARGE SIEVE' METHOD AND ITS APPLICATIONS IN THE THEORY OF NUMBERS
THE 'LARGE SIEVE' METHOD AND ITS APPLICATIONS IN THE THEORY OF NUMBERS
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“大筛”法及其在数论中的应用
DOI：
10.1070/rm1966v021n01abeh004146
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发表时间：
1966
影响因子：
0.9
通讯作者：
M. Barban
中科院分区：
文献类型：
--
作者：
M. Barban
内容简介第一节：本方法的实质。第一应用§2.“大筛”的概率解释§3.复合模数。二元加法问题的应用§4.L函数在σ=1线附近的非零性.§5.具有负行列式的本原二次型的个数分布定理§6.素数的ΣR等分布.A·Selberg的S筛子的应用§7.关于ΣR-等分布序列的多项式的值集上给出的加性算术函数的中心极限定理§8.关于ΣR-等分布序列的多项式的值集上乘法函数的均值的阶参考文献
CONTENTSNotationIntroduction § 1. The essence of the method. First applications § 2. The probabilistic interpretation of the 'large sieve' § 3. Composite moduli. Application to binary additive problems § 4. The non-vanishing of L-functions near the line σ = 1 § 5. A distribution theorem for the number of classes of primitive quadratic forms with negative determinant § 6. ΣR-equidistribution of prime numbers. Application to A. Selberg' s sieve § 7. The central limit theorem for additive arithmetic functions, given on the set of values of a polynomial for a ΣR-equidistributed sequence § 8. The order of the mean values of multiplicative functions on the set of values of a polynomial for a ΣR-equidistributed sequenceReferences