On squares in polynomial products

Let f(X) ∈ ℤ[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadr...

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Detalles Bibliográficos
Autores: Cilleruelo, Javier, Luca, Florian, Quirós Gracián, Adolfo, Shparlinski, Igor E.
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/710672
Acceso en línea:http://hdl.handle.net/10486/710672
https://dx.doi.org/10.1007/s00605-008-0066-y
Access Level:acceso abierto
Palabra clave:character sums
quadratic fields
square sieve
Matemáticas
Descripción
Sumario:Let f(X) ∈ ℤ[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadratic fields of the form ℚ(√F (n)), n = M + 1, ..., M + N