Square-free values of f(p), f cubic

• 成果类型: Article
• 署名作者: Helfgott, Harald Andres
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-014-0117-2
• 发表日期: 2014
• 页码: 107-135
• 关键词: power-free values; elliptic-curves; integral points; THEOREM

摘要

Let , . Assume that f does not have repeated roots. Assume as well that, for every prime q, mod q (2) has at least one solution in . Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.