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Современные проблемы теории чисел
5 марта 2015 г. 12:45, г. Москва, МИАН, комн. 530 (ул. Губкина, 8)
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"Reducible polynomials of bounded height"
А. Дубицкас Department of Mathematical Computer Science, Vilnius University
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Эта страница: | 195 |
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Аннотация:
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).
Язык доклада: английский
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