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Refined configuration results for extremal Type II lattices of ranks $ 40$ and $ 80$


Authors: 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
Published electronically: August 27, 2009
MathSciNet review: 2550174
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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

DOI: https://doi.org/10.1090/S0002-9939-09-10063-1
Keywords: Type II lattice, extremal lattice, weighted theta function, spherical design, configuration result
Received by editor(s): May 29, 2009
Published electronically: August 27, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 Noam D. Elkies and Scott Duke Kominers