On an equation with prime numbers
On an equation with prime numbers
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DOI：
10.4064/aa-83-2-117-126
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发表时间：
1998
期刊：
影响因子：
0.7
通讯作者：
A. Kumchev;T. Nedeva
中科院分区：
文献类型：
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作者：
A. Kumchev;T. Nedeva
其中c>；1不是整数，并且证明了在两种情况下都存在k0(C)，使得当k≥k0和N足够大时，相应的问题有解。后来，Deshouillers[4]和Arhipov和Zitkov[1]改进了西格尔在(2)中的结果。人们还可以提到Deshouillers[5]和Gritsenko[7]的论文，其中考虑了两个变量的方程(2)。1952年，I.I.Piatetski-Shapiro[12]与x1一起考虑了(1)。。。，XK仅限于素数。设H(C)表示最小k，使得具有固定e>；0的不等式(1)对每个足够大的实数N都有素数解。Piatetski-Shapiro证明了
where c > 1 is not integer, and proved in both cases that there exists k0(c) such that the corresponding problem has solutions if k ≥ k0 and N is sufficiently large. Later Deshouillers [4] and Arhipov and Zhitkov [1] improved Segal’s result on (2). One may also mention the papers of Deshouillers [5] and Gritsenko [7], where the equation (2) in two variables was considered. In 1952 I. I. Piatetski–Shapiro [12] considered (1) with x1, . . . , xk restricted to prime numbers. Let H(c) denote the least k such that the inequality (1) with fixed e > 0 has solutions in prime numbers for every sufficiently large real N . Piatetski–Shapiro proved that