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arXiv · 1901.09014

On the number of primes for which a polynomial is Eisenstein

Shilin Ma·Kevin McGown·Devon Rhodes·Mathias Wanner
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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 $\psi(f)$ denote the number of primes for which a polynomial $f$ is Eisenstein. We give expressions for the mean and variance of the function $\psi$ for each fixed degree, where the polynomials are ordered according to their height.

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Shilin Ma, Kevin McGown, Devon Rhodes, Mathias Wanner. 2019-01-25. On the number of primes for which a polynomial is Eisenstein. https://arxiv.org/abs/1901.09014

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