The density of polynomials of degree n over Zp having exactly r roots in Qp

Stevan Gajovic; Manjul Bhargava; John Cremona; Tom Fisher

The density of polynomials of degree n over Zp having exactly r roots in Qp

Stevan Gajovic, Manjul Bhargava, John Cremona, Tom Fisher

Algebra

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We determine the probability that a random polynomial of degree n over Zp has exactly r roots in Qp, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.

Originele taal-2	English
Uitgever	arXiv
Aantal pagina's	19
Status	Submitted - 26-jan.-2021

Publicatie series

Naam	ArXiv
Uitgeverij	Cornell University Press
ISSN van geprinte versie	2331-8422

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https://arxiv.org/abs/2101.09590

Citeer dit

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AU - Gajovic, Stevan

AU - Bhargava, Manjul

AU - Cremona, John

AU - Fisher, Tom

PY - 2021/1/26

Y1 - 2021/1/26

N2 - We determine the probability that a random polynomial of degree n over Zp has exactly r roots in Qp, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.

AB - We determine the probability that a random polynomial of degree n over Zp has exactly r roots in Qp, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.

UR - https://arxiv.org/abs/2101.09590

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BT - The density of polynomials of degree n over Zp having exactly r roots in Qp

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