LLL: a tool for effective diophantine approximation

Guillaume Hanrot 1
1 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The purpose of this paper is to survey in a unified setting some of the results in diophantine approximation that the LLL algorithm can make effective in an efficient way. We mostly study the problems of finding good rational approximations to vectors of real and p-adic numbers, and of finding approximate linear relations between vectors of real numbers. We also discuss classical applications of those eective versions, among which Mertens' conjecture and the effective solution of diophantine equations.
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Contributor : Guillaume Hanrot <>
Submitted on : Thursday, November 15, 2007 - 2:15:19 PM
Last modification on : Thursday, January 11, 2018 - 6:21:04 AM


  • HAL Id : inria-00187880, version 1



Guillaume Hanrot. LLL: a tool for effective diophantine approximation. Conference in honour of the 25th birthday of the LLL algorithm - LLL+25, Jun 2007, Caen, France. ⟨inria-00187880⟩



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