Polynomials with Special Regard to Reducibility

By Andrzej Schinzel. 2000

327 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a770ba5a8756a8948f09a67eaa9b66a3a3251542

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Citations in the corpus

Solution of the polynomial moment problem (2007, background): “nimal idempotent E∈ Vk(TH) corresponds an irreducible subspace V = Im{E}. In general, the decomposition of kn into a sum of TH-invariant irreducible subspaces is not uniquely deﬁned. Nevertheless, if (26) kn = V⊕a1 1 ⊕···⊕V ⊕ar r isa decompositionsuch that Vi,1 ≤ i≤ r,arepairwisenon-isomorphicTH-inv”
A Strong Tits Alternative (2008, background): “Recall Bezout’s theorem about the intersection of finitely many algebraic subvarieties (see for instance [35]), namely:”
Number Theory and Polynomials: The Mahler measure of algebraic numbers: a survey (2007, unknown): “Books covering various aspects of Mahler measure include the following: Bertin and PathiauxDelefosse [14], Bertin et al [15], Bombieri and Gubler [18], Borwein [22], Schinzel [131], Schinzel [134], Waldschmidt [156].”
Intersections of polynomial orbits, and a dynamical Mordell–Lang conjecture (2007, background): “The fundamental results in this topic were proved by Ritt in the 1920’s [20]; for more recent developments, see [16,22].”
Center conditions at infinity for Abel differential equations (2010, methodology): “This proposition follows in a straightforward way from the results of Ritt (see [57], [62]).”
Anomalous Subvarieties—Structure Theorems and Applications (2007, methodology): “The general conjecture was proved by the first and third authors in [24].”
On the Hilbert property and the fundamental group of algebraic varieties (2016, background): “In this case (or more generally when k is finitely generated over the prime field) the HP is known to hold for projective spaces (Hilbert [20]), for which several proofs are available (see [5], [15], [22], [27], [28], [29], [37]).”