Unlikely intersections and multiple roots of sparse polynomials
نویسندگان
چکیده
منابع مشابه
Efficiently Computing Real Roots of Sparse Polynomials
We propose an efficient algorithm to compute the real roots of a sparse polynomial f ∈ R[x] having k non-zero realvalued coefficients. It is assumed that arbitrarily good approximations of the non-zero coefficients are given by means of a coefficient oracle. For a given positive integer L, our algorithm returns disjoint disks ∆1, . . . ,∆s ⊂ C, with s < 2k, centered at the real axis and of radi...
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Combining ideas of Ihara-Serre-Tate, Lang [5] proved the following natural result. If a (complex, irreducible) plane curve C ⊂ A contains infinitely many points with both coordinates roots of unity, then C is the zero locus of an equation of the form xy = ζ, where a, b ∈ Z and ζ is a root of unity. In other words, if F ∈ C[x, y] is an irreducible polynomial for which there exist infinitely many...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2017
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-017-1860-9