|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Extractors in Paley graphs: a random model | | Rudi Mrazović
; | | Date: |
20 Oct 2015 | | Abstract: | A well-known conjecture in analytic number theory states that for every pair
of sets $X,Ysubsetmathbb{Z}/pmathbb{Z}$, each of size at least $log ^C p$
(for some constant $C$) we have that for $(frac12+o(1))|X||Y|$ of the pairs
$(x,y)in X imes Y$, $x+y$ is a quadratic residue modulo $p$. We address the
probabilistic analogue of this question, that is for every fixed $delta>0$,
given a finite group $G$ and $Asubset G$ a random subset of density $frac12$,
we prove that with high probability for all subsets $|X|,|Y|geq log
^{2+delta} |G|$ for $(frac12+o(1))|X||Y|$ of the pairs $(x,y)in X imes Y$
we have $xyin A$. | | Source: | arXiv, 1510.5998 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER