On the distribution of lengths of short vectors in a random lattice
Abstract
We use an idea from sieve theory to estimate the distribution of the lengths of $k$th shortest vectors in a random lattice of covolume 1 in dimension $n$. This is an improvement of the results of Rogers and Södergren in that it allows $k$ to increase with $n$.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- arXiv:
- arXiv:1410.2005
- Bibcode:
- 2014arXiv1410.2005K
- Keywords:
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- Mathematics - Number Theory