On a problem of Sárközy and Sós for multivariate linear forms
We prove that for pairwise co-prime numbers k1,…,kd=2 there does not exist any infinite set of positive integers A such that the representation function rA(n)=# {(a1,…,ad)¿Ad:k1a1+¿ +kdad=n} becomes constant for n large enough. This result is a particular case of our main theorem, which poses a furt...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/345505 |
| Acceso en línea: | https://hdl.handle.net/2117/345505 https://dx.doi.org/10.4171/rmi/1193 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial number theory Representation function Classificació AMS::11 Number theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We prove that for pairwise co-prime numbers k1,…,kd=2 there does not exist any infinite set of positive integers A such that the representation function rA(n)=# {(a1,…,ad)¿Ad:k1a1+¿ +kdad=n} becomes constant for n large enough. This result is a particular case of our main theorem, which poses a further step towards answering a question of Sárközy and Sós and widely extends a previous result of Cilleruelo and Rué for bivariate linear forms. |
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