山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (2): 39-43.doi: 10.6040/j.issn.1671-9352.0.2016.125
李芳,关爱霞,李国全*
LI Fang, GUANG Ai-xia, LI Guo-quan*
摘要: 对于有限Abel群G与A,B⊂G,证明了存在Bohr集B(Γ,δ)与常数D>0满足: ∠T⊂B(Γ,δ),若|T|≤D,则A+B中含有T的平移。
中图分类号:
[1] BOURGAIN J. Roth’s theorem on progressions revisited[J]. J Anal Math, 2008, 104:155-192. [2] CROOT E, ŁABA I, SISASK O. Arithmetic progressions in sumsets and Lp-almost-periodicity[J]. Combin Probab Comput, 2013, 22:351-365. [3] GREEN B. Arithmetic progressions in sumsets[J]. Geom Funct Anal, 2002, 12: 584-597. [4] RUZSA I. Arithmetic progressions in sumsets[J]. Acta Arith, 1991, 60:191-202. [5] SANDERS T. Additive structures in sumsets[J]. Math Proc Cambridge Philos Soc, 2008, 144:289-316. [6] GREEN B. Finite field models in arithmetic combinatorics[M] //Surveys in Combinatorics 2005. Cambridge: Cambridge University Press, 2005:1-27. [7] TAO T, VU V. Additive combinatorics[M]. Cambridge: Cambridge University Press, 2006. |
[1] | 曹亚萌,黎娇,李国全. 有限域上的和集与子空间的平移[J]. 山东大学学报(理学版), 2018, 53(4): 7-10. |
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