

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

