Mathematische Zeitschrift

, Volume 282, Issue 3–4, pp 1117–1126 | Cite as

On the distribution of lengths of short vectors in a random lattice

Article
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Abstract

We use an idea from sieve theory—specifically, an inclusion–exclusion argument inspired by Schmidt (Proc Am Math Soc 9:390–403, 1958)—to estimate the distribution of the lengths of kth shortest vectors in a random lattice of covolume 1 in dimension n. This is an improvement of the results of Rogers (Proc Lond Math Soc 6(3):305–320, 1956) and Södergren (Math Z 269:945–954, 2011) in that it allows k to increase with n.

Keywords

Lattice Vector Integration Formula Nonzero Vector Invariant Probability Measure Random Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Korea Institute of Advanced StudySeoulKorea

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