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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Refined configuration results for extremal Type II lattices of ranks $40$ and $80$
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by Noam D. Elkies and Scott Duke Kominers PDF
Proc. Amer. Math. Soc. 138 (2010), 105-108

Abstract:

We show that, if $L$ is an extremal Type II lattice of rank $40$ or $80$, then $L$ is generated by its vectors of norm $\operatorname {min}(L)+2$. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices $L$ are generated by their vectors of norms $\operatorname {min}(L)$ and $\operatorname {min}(L)+2$.
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Additional Information
  • Noam D. Elkies
  • Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
  • Email: elkies@math.harvard.edu
  • Scott Duke Kominers
  • Affiliation: Department of Mathematics and Department of Economics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
  • Address at time of publication: 8520 Burning Tree Road, Bethesda, Maryland 20817
  • Email: kominers@fas.harvard.edu, skominers@gmail.com
  • Received by editor(s): May 29, 2009
  • Published electronically: August 27, 2009
  • Communicated by: Ken Ono
  • © Copyright 2009 Noam D. Elkies and Scott Duke Kominers
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 105-108
  • MSC (2000): Primary 11H55; Secondary 05B30, 11F11
  • DOI: https://doi.org/10.1090/S0002-9939-09-10063-1
  • MathSciNet review: 2550174