On an additive representation function

✍ Scribed by R. Balasubramanian; Gyan Prakash

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 204 KB
• Volume: 104
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2003.09.004

✦ Synopsis

Let A be an infinite subset of natural numbers, nAN and X a positive real number. Let rðnÞ denotes the number of solution of the equation n ¼ a 1 þ a 2 where a 1 pa 2 and a 1 ; a 2 AA: Also let jAðX Þj denotes the number of natural numbers which are less than or equal to X and belong to A: For those A which satisfy the condition that for all sufficiently large natural numbers n we have rðnÞa1; we improve the lower bound of jAðX Þj given by Nicolas et. al.

[NRS98]. The bound which we obtain is essentially best possible.