Using zeta functions to factor polynomials over finite fields

DOI10.1090/conm/722/14528zbMath1468.11247arXiv1710.00970OpenAlexW2963635493MaRDI QIDQ5236842

Bjorn Poonen

Publication date: 16 October 2019

Published in: Arithmetic Geometry: Computation and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00970

zbMATH Keywords

finite fieldsabelian varietyfactoring polynomialszeta function

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Polynomials over finite fields (11T06) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Arithmetic ground fields for abelian varieties (14K15)

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Cites Work

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• Calculability of étale cohomology modulo \(\ell\)
• Real polynomials with all roots on the unit circle and abelian varieties over finite fields
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• Maps between curves and arithmetic obstructions
• Factoring Polynomials Over Large Finite Fields
• Factoring polynomials over finite fields: A survey

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