By Henri Darmon (auth.), Guillaume Hanrot, François Morain, Emmanuel Thomé (eds.)
This booklet constitutes the refereed court cases of the ninth overseas Algorithmic quantity thought Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised complete papers offered including five invited papers have been conscientiously reviewed and chosen for inclusion within the publication. The papers are dedicated to algorithmic points of quantity idea, together with user-friendly quantity concept, algebraic quantity thought, analytic quantity thought, geometry of numbers, algebraic geometry, finite fields, and cryptography.