几乎收敛的0-1序列与素数

IF 0.7 4区数学 Q2 MATHEMATICS

Siberian Mathematical Journal Pub Date : 2023-11-24 DOI:10.1134/s0037446623060174

N. N. Avdeev

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引用次数: 0

摘要

我们研究了0-1序列，并建立了该序列上的上下sucheon泛函的值与序列支持中元素的所有可能约数的集合之间的联系。如果0-1序列支持中所有元素的简约数集合的并集是有限的，则该序列几乎收敛于零。研究了0-1序列，其支撑点恰好由给定集合中元素的倍数构成，并建立了该序列上的一类泛函等于1的充分必要条件。我们证明了存在无穷多个序列上的下萨克森泛函为1，并且下萨克森泛函在任何这样的序列上都不会消失。

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Almost Convergent 0-1-Sequences and Primes

We study 0-1-sequences and establish the connection between the values of the upper and lower Sucheston functional on such sequence and the set of all possible divisors of the elements in the sequence support. If the union of the sets of all simple divisors of the elements in a 0-1-sequence support is finite then the sequence is almost convergent to zero. We study the 0-1-sequences whose support consists exactly of the multiples of the elements in a given set, and establish some necessary and sufficient conditions for the upper Sucheston functional to be equal to 1 on such sequence. We prove that there are infinitely many sequences at which the lower Sucheston functional is 1, and the lower Sucheston functional never vanishes at any of such sequences.

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来源期刊

Siberian Mathematical Journal 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Siberian Mathematical Journal is journal published in collaboration with the Sobolev Institute of Mathematics in Novosibirsk. The journal publishes the results of studies in various branches of mathematics.