Acta Mathematica

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

Harald Andrés Helfgott

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Abstract

Let fZ[x], degf=3. Assume that f does not have repeated roots. Assume as well that, for every prime q, f(x)0 mod q2 has at least one solution in (Z/q2Z). Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.

Article information

Source
Acta Math., Volume 213, Number 1 (2014), 107-135.

Dates
Received: 29 June 2012
Revised: 28 May 2013
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485801837

Digital Object Identifier
doi:10.1007/s11511-014-0117-2

Mathematical Reviews number (MathSciNet)
MR3261012

Zentralblatt MATH identifier
1316.11084

Rights
2014 © Institut Mittag-Leffler

Citation

Helfgott, Harald Andrés. Square-free values of f ( p ), f cubic. Acta Math. 213 (2014), no. 1, 107--135. doi:10.1007/s11511-014-0117-2. https://projecteuclid.org/euclid.acta/1485801837


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