Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice

@article{Lagarias1990KorkinZolotarevBA,
  title={Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice},
  author={Jeffrey C. Lagarias and Hendrik W. Lenstra and Claus-Peter Schnorr},
  journal={Combinatorica},
  year={1990},
  volume={10},
  pages={333-348}
}
Let Aj(L), Aj(L*) denote the successive minima of a lattice L and its reciprocal lattice L*, and let [bj,. ., bn] be a basis of L that is reduced in the sense of Korkin and Zolotarev. We prove that [4/(t + 3)]A,(L) < | b j 2 < [(t + 3)/4]A t(i) 2 and | b J 2 A „ ^ + 1 ( L * ) 2 < [(, + 3)/4][(n ι + 4)/4] 7 * 2 , where 7^ = min{7j : l < j < n} and 7^ denotes Hermite's constant. As a consequence the inequalities l < \(L)\n_t+1(L*) < n 2 /6 are obtained for n > 7. Given a basis S of a lattice L in… CONTINUE READING
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