A variant of Tao';s method with application to restricted sumsets

作者：Guo Song^*; Sun Zhi Wei

来源：Journal of Number Theory, 2009, 129(2): 434-438.

DOI：10.1016/j.jnt.2008.05.009

• Restricted sumsets
• Uncertainty principle
• Erdos-Heilbronn conjecture

In this paper, we develop Terence Tao';s harmonic analysis method and apply it to restricted sumsets. The well-known Cauchy-Davenport theorem asserts that if N not equal A, B subset of Z/pZ with p a prime, then vertical bar A B vertical bar >= min{p, vertical bar A vertical bar vertical bar B vertical bar - 1), where A B = {a b; a epsilon A. b epsilon B}. In 2005, Terence Tao gave a harmonic analysis proof of the Cauchy-Davenport theorem, by applying a new form of the uncertainty principle on Fourier transform. We modify Tao';s method so that it can be used to prove the following extension of the Erdos-Heilbronn conjecture: If A, B, S are non-empty subsets of Z/pZ with p a prime, then vertical bar{a b; a epsilon A, b epsilon B, a - b is not an element of S}vertical bar >= min{p, vertical bar A vertical bar vertical bar B vertical bar - 2 vertical bar S vertical bar - 1).

• 出版日期2009-2
• 单位南京大学; 淮阴师范学院