A variant of Tao's method with application to restricted sumsets
| dc.creator | Guo, Song | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2008-08-02 | |
| dc.date | 2008-11-28 | |
| dc.date.accessioned | 2026-07-07T12:04:59Z | |
| dc.date.available | 2026-07-07T12:04:59Z | |
| dc.description | 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 $A$ and $B$ are nonempty subsets of $Z/pZ$ with $p$ a prime, then $|A+B|\ge min{p,|A|+|B|-1}$, where $A+B={a+b: a\in A, b\in B}$. 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 nonempty subsets of $Z/pZ$ with $p$ a prime, then $|{a+b: a\in A, b\in B, a-b not\in S}|\ge min {p,|A|+|B|-2|S|-1}$. | |
| dc.identifier | https://arxiv.org/abs/0808.0243 | |
| dc.identifier | http://arxiv.org/abs/0808.0243 | |
| dc.identifier | J. Number Theory 129(2009), no.2, 434-438 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208267 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B75; 05A05; 11P99; 11T99 | |
| dc.title | A variant of Tao's method with application to restricted sumsets | |
| dc.type | text |