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...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2008 |
| País: | España |
| Recursos: | Universidad Autónoma de Madrid |
| Repositório: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.uam.es:10486/710672 |
| Acesso em linha: | http://hdl.handle.net/10486/710672 https://dx.doi.org/10.1007/s00605-008-0066-y |
| Access Level: | Acceso aberto |
| Palavra-chave: | character sums quadratic fields square sieve Matemáticas |
| Resumo: | 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 |
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