The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments

DOI10.1142/S1793042115500396zbMath1337.11065WikidataQ123126945 ScholiaQ123126945MaRDI QIDQ5248573

Hector Pasten

Publication date: 8 May 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

ABC conjectureprimes in arithmetic progressionsquarefree values of polynomials

Mathematics Subject Classification ID

Applications of sieve methods (11N36) Primes in congruence classes (11N13) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items (16)

Monogenic Pisot and anti-Pisot polynomials ⋮ RECIPROCAL MONOGENIC QUINTINOMIALS OF DEGREE ⋮ Monogenic reciprocal trinomials and their Galois groups ⋮ Infinite families of monogenic trinomials and their Galois groups ⋮ Monogenic binomial compositions ⋮ Infinite families of monogenic quadrinomials, quintinomials and sextinomials ⋮ Minimal Mahler measure in cubic number fields ⋮ Infinite families of non-monogenic trinomials ⋮ Monogenic polynomials with non-squarefree discriminant ⋮ Sextic reciprocal monogenic dihedral polynomials ⋮ Unnamed Item ⋮ A BRIEF NOTE ON SOME INFINITE FAMILIES OF MONOGENIC POLYNOMIALS ⋮ Infinite families of reciprocal monogenic polynomials and their Galois groups ⋮ Orders of units in integral group rings and blocks of defect 1 ⋮ Some new infinite families of monogenic polynomials with non-squarefree discriminant ⋮ Monogenic trinomials with non-squarefree discriminant

Cites Work

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• Erratum to ``The primes contain arbitrarily long polynomial progressions
• The primes contain arbitrarily long polynomial progressions
• Powerful values of polynomials and a conjecture of Vojta
• \(ABC\) implies no ``Siegel zeros for \(L\)-functions of characters with negative discriminant
• The primes contain arbitrarily long arithmetic progressions
• Diophantine Approximation and Nevanlinna Theory
• Counting squarefree values of polynomials with error term

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