Values of polynomials with integer coefficients and distance to their common zeros
نویسندگان
چکیده
منابع مشابه
Polynomials with integer coefficients and their zeros
We study several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to the approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets. The distribution of zeros for...
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For fixed ` ≥ 2, fixed positive integers m1 > m2 with gcd(m1,m2) = 1 and n1 > n2 > · · · > n` with gcd(n1, . . . , n`) = 1, and fixed rationals a1, a2, . . . , a`+1, b1, b2 which are all nonzero except for possibly a`+1, we show the finiteness of integral solutions x, y of the equation a1x n1 + · · ·+ a`x` + a`+1 = b1y + b2y , when n1 ≥ 3, m1 ≥ 2`(` − 1), and (n1, n2) 6= (m1,m2). In relation to...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1994
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-68-2-101-112