p+2^(k)型表法个数不超过K的正整数的渐近密度

Asymptotic Density of Positive Integers Which Have at Most K Distinct Representations of the Form p+2^(k)

能够表为p+2^(k)型的正整数的渐近密度问题是组合数论研究中的一个重要问题,它与著名的Goldbach-Linnik问题密切相关.我们研究了能够表为p+2^(k)形式的正整数的表示方法个数不超过K的正整数集合AK的元素的比例问题,进一步改进了现有结论,获得了一些更好的下界.

The asymptotic density of positive integers in the form of p+2^(k),is an important problem in the study of combinatorial number theory.It is closely related to the well-known Goldbach-Linnik problem.In this paper,we study the asymptotic density of positive integers which have at most K distinct representations of the form p+2^(k).The existing conclusions are further improved,and some better lower bounds are obtained.