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- W3214548323 abstract "Let $f$ and $g$ be two monic polynomials with integer coefficients and nonzero resultant $r$. Assume that $v_p(f(n))ge s_1$ and $v_p(g(n))ge s_2$ hold for all integers $n$ for some $s_1, s_2$ fixed non-negative integers. Let $S$ denote the maximum of $v_p(gcd(f(n),g(n)))$ over all integers $n$. In this paper, we establish multiple lower bound for $v_p(r)$. More specifically, we show that $v_p(r)ge S-max{s_1,s_2}+ps_1s_2frac{p-1}{p-p^{-k}}$, where $k=lfloor log_p((p-1)max{s_1,s_2}+1)rfloor -1$." @default.
- W3214548323 created "2021-11-22" @default.
- W3214548323 creator A5032405136 @default.
- W3214548323 date "2021-11-11" @default.
- W3214548323 modified "2023-09-27" @default.
- W3214548323 title "Estimating the $p$-adic valuation of the resultant" @default.
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- W3214548323 hasPublicationYear "2021" @default.
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