Showing papers by "Roger A. Horn published in 1962"
TL;DR: In this article, the authors consider polynomials in one variable with all coefficients integral and leading coefficients positive, their degrees being hi, h2, **, hk respectively, and assume that each polynomial is irreducible over the field of rational numbers and no two of them differ by a constant factor.
Abstract: Suppose fi, f2, -*, fk are polynomials in one variable with all coefficients integral and leading coefficients positive, their degrees being hi, h2, **. , hk respectively. Suppose each of these polynomials is irreducible over the field of rational numbers and no two of them differ by a constant factor. Let Q(fi , f2, ... , fk ; N) denote the number of positive integers n between 1 and IV inclusive such that fi(n) , f2(n), , fk(n) are all primes. (We ignore the finitely many values of n for which some fi(n) is negative.) Then heuristically we would expect to have for N large
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