ON THE SUM OF CONSECUTIVE INTEGERS IN SEQUENCES II

被引：0
|
作者：
Tsai, Mu-Tsun [1 ]
Zaharescu, Alexandru [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2012年 / 8卷 / 05期
基金：
美国国家科学基金会;
关键词：
Consecutive integer; arithmetic progression; prime number; representation;
D O I：
10.1142/S1793042112500753
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A be a sequence of natural numbers, r(A)(n) be the number of ways to represent n as a sum of consecutive elements in A, and M-A(x) := Sigma(n <= x) r(A)(n). We give a new short proof of LeVeque's formula regarding M-A(x) when A is an arithmetic progression, and then extend the proof to give asymptotic formulas for the case when A behaves almost like an arithmetic progression, and also when A is the set of primes in an arithmetic progression.
引用
收藏
页码：1281 / 1299
页数：19
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