Prime valued polynomials and class numbers of quadratic fields.

Mollin, Richard A.

Displaying similar documents to “Prime valued polynomials and class numbers of quadratic fields.”

Knebusch-Milnor exact sequence and parity of class numbers

Kazimierz Szymiczek (1996)

Acta Mathematica et Informatica Universitatis Ostraviensis

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Imaginary quadratic fields satisfying the Hilbert-Speiser type condition for a small prime p

Humio Ichimura, Hiroki Sumida-Takahashi (2007)

Acta Arithmetica

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Prime factors of values of polynomials

J. Browkin, A. Schinzel (2011)

Colloquium Mathematicae

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We prove that for every quadratic binomial f(x) = rx² + s ∈ ℤ[x] there are pairs ⟨a,b⟩ ∈ ℕ² such that a ≠ b, f(a) and f(b) have the same prime factors and min{a,b} is arbitrarily large. We prove the same result for every monic quadratic trinomial over ℤ.

Frobenius distributions for real quadratic orders

Peter Stevenhagen (1995)

Journal de théorie des nombres de Bordeaux

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We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.