Addition of sets of integers of positive density

被引：18
|
作者：
Bilu, Y
机构：
[1] UNIV BORDEAUX 2,F-33076 BORDEAUX,FRANCE
[2] UNIV GOTTINGEN,MATH INST SFB170,D-37073 GOTTINGEN,GERMANY
来源：
JOURNAL OF NUMBER THEORY | 1997年 / 64卷 / 02期
关键词：
D O I：
10.1006/jnth.1997.2123
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A be a set of nonnegative integers, <(d)under bar(A)> its lower asymptotic density, and A + A = {a + a': a, a' is an element of A}. A classical theorem of Kneser completely describes the structure of all sets A subject to (d) under bar(A + A)<2 (d) under bar A. Freiman succeeded in partial generalization of Kneser's theorem when 2 is replaced by an arbitrary number. Going further in this direction, we obtain a mon precise version of Freiman's result. (C) 1997 Academic Press.
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收藏
页码：233 / 275
页数：43
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