On the number of primes for which a polynomial is Eisenstein
Abstract
Previously Heyman and Shparlinski gave an asymptotic formula with error term for the number of Eisenstein polynomials of fixed degree and bounded height. Let (f) denote the number of primes for which a polynomial f is Eisenstein. We give expressions for the mean and variance of the function for each fixed degree, where the polynomials are ordered according to their height.
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