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,...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:2117/121761 |
| Acceso en línea: | https://hdl.handle.net/2117/121761 https://dx.doi.org/10.1016/j.endm.2018.06.018 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial analysis additive combinatorics representation functions additive basis Anàlisi combinatòria Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| 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 S´ark¨ozy and S´os and widely extends a previous result of Cilleruelo and Ru´e for bivariate linear forms (Bull. of the London Math. Society 2009). |
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