On the number of Eisenstein polynomials of bounded height

Randell Heyman, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree d and of height at most H, as H → ∞. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most H.

Original languageEnglish
Pages (from-to)149-156
Number of pages8
JournalApplicable Algebra in Engineering, Communications and Computing
Issue number2
Publication statusPublished - Jun 2013


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