A step beyond Freiman’s theorem for set addition modulo a prime"
Freiman’s 2.4-Theorem states that any set A ⊂ Z p satisfying |2A| ≤ 2.4|A| − 3 and |A| < p/35 can be covered by an arithmetic progression of length at most |2A| − |A| + 1. A more general result of Green and Ruzsa implies that this covering property holds for any set satisfying |2A| ≤ 3|A| − 4 as...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/530645 |
| Acesso em linha: | http://hdl.handle.net/2072/530645 |
| Access Level: | acceso abierto |
| Palavra-chave: | Matemàtiques 51 |
| Resumo: | Freiman’s 2.4-Theorem states that any set A ⊂ Z p satisfying |2A| ≤ 2.4|A| − 3 and |A| < p/35 can be covered by an arithmetic progression of length at most |2A| − |A| + 1. A more general result of Green and Ruzsa implies that this covering property holds for any set satisfying |2A| ≤ 3|A| − 4 as long as the rather strong density requirement |A| < p/10 215 is satisfied. We present a version of this statement that allows for sets satisfying |2A| ≤ 2.48|A| − 7 with the more modest density requirement of |A| < p/10 10 . |
|---|