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- W2020189493 abstract "P. Turán asked if there exists an absolute constant $C$ such that for every polynomial $fin mathbb {Z}[x]$ there exists an irreducible polynomial $gin mathbb {Z}[x]$ with $deg (g)leq deg (f)$ and $L(f-g)leq C$, where $L(cdot )$ denotes the sum of the absolute values of the coefficients. We show that $C=5$ suffices for all integer polynomials of degree at most $40$ by investigating analogous questions in $mathbb {F}_p[x]$ for small primes $p$. We also prove that a positive proportion of the polynomials in $mathbb {F}_2[x]$ have distance at least $4$ to an arbitrary irreducible polynomial." @default.
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- W2020189493 date "2012-09-01" @default.
- W2020189493 modified "2023-10-18" @default.
- W2020189493 title "The distance to an irreducible polynomial, II" @default.
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- W2020189493 doi "https://doi.org/10.1090/s0025-5718-2011-02555-x" @default.
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