Power-free values of polynomials

DOI10.1007/s00013-011-0224-7zbMath1252.11070OpenAlexW1977257638MaRDI QIDQ633178

Timothy D. Browning

Publication date: 31 March 2011

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-011-0224-7

zbMATH Keywords

rational pointsirreducible polynomialspower-free valuesaffine hypersurfaces

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items (15)

Towards van der Waerden’s conjecture ⋮ On the average value of the canonical height in higher dimensional families of elliptic curves ⋮ Square-free values of polynomials over the rational function field ⋮ Starting with gaps between k-free numbers ⋮ Counting rational points on projective varieties ⋮ Square-free values of \(n^2 + n + 1\) ⋮ Small generators of quadratic fields and reduced elements ⋮ Square-free values of \(f(p)\), \(f\) cubic ⋮ On the \(k\)-free values of the polynomial \(xy^k + C\) ⋮ On the representation of \(k\)-free integers by binary forms ⋮ DENSITY OF POWER‐FREE VALUES OF POLYNOMIALS ⋮ POWER-FREE VALUES OF THE POLYNOMIAL t₁⋯t_r−1 ⋮ Enumerative Galois theory for cubics and quartics ⋮ Power‐free values of polynomials ⋮ Rational points and prime values of polynomials in moderately many variables

Cites Work

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• Power-free values, large deviations, and integer points on irrational curves
• Powerfree values of binary forms
• Counting Rational Points on Algebraic Varieties
• Power-free values, repulsion between points, differing beliefs and the existence of error
• POWER-FREE VALUES OF BINARY FORMS
• Power free values of polynomials
• Power Free Values of Polynomials II
• The Square-Free Sieve and the Rank of Elliptic Curves
• Counting rational points on hypersurfaces
• On the power free values of polynomials
• Arithmetical Properties of Polynomials

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