Advances in additive number theory

IF 0.4 Q4 MATHEMATICS Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-26 DOI:10.5269/bspm.51233
José Alfonso López Nicolás
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Abstract

We obtain sufficient conditions to know if given a positive even integer number and a set of positive integer numbers being all even or all odd, such a number can be expressed as sum of two elements of this set. As consequence we obtain a result which, when applied to the prime numbers set, would prove Goldbach's Conjecture provided that certain conditions are satisfied. These hypothesis include Prime Consecutive Conjecture, which is a generalized form of Twin Prime Conjecture. In addition, we extend these results to sets of positive real numbers, even for two different sets. We also obtain a recurrent approximation of \pi(x) for enough large real x, being \pi the distribution function of the prime number set, which uses whichever expression of x as product of enough large factors. We also state this approximation in a more general context, give upper and lower bounds for the error, and show that this approximation is asymptotically equivalent to \pi(x).
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加性数论的进展
我们得到了足够的条件来知道给定一个正偶数和一组正整数是否都是偶数或都是奇数,这样的数字可以表示为这个集合的两个元素的和。因此,我们得到了一个结果,当应用于素数集时,只要满足某些条件,就会证明哥德巴赫猜想。这些假设包括素数连续猜想,它是双素数猜想的一种推广形式。此外,我们将这些结果推广到正实数集,即使是两个不同的集。对于足够大的实数x,我们还获得了\pi(x)的递归近似,\pi是素数集的分布函数,它使用x的任意表达式作为足够大因子的乘积。我们还在更一般的上下文中陈述了这种近似,给出了误差的上界和下界,并证明了这种近似渐近等价于\pi(x)。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
140
审稿时长
25 weeks
期刊最新文献
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