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Contemporary Problems in Number Theory
March 5, 2015 12:45, Moscow, Steklov Mathematical Institute, Room 530 (8 Gubkina)
 


"Reducible polynomials of bounded height"

A. Dubickas

Department of Mathematical Computer Science, Vilnius University

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Abstract: We obtain an asymptotic formula for the number of reducible integer polynomials of degree $d$ and of height at most $T$ as $T \to \infty$. For each $d \geq 3$ the main term turns out to be of the form $c_d T^d$, where the constant $c_d$ is given in terms of some infinite Dirichlet series involving volumes of symmetric convex bodies in $R^d$. Earlier results in this direction were given by van der Waerden (1934), Polya and Szego, Chela (1963), Dorge (1965) and Kuba (2009).

Language: English

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