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Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80

By: Noam D. Elkies and Scott Duke Kominers

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 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... View Details

Keywords: Mathematical Methods

September 2009
Article

Finding Matrices that Satisfy Functional Equations

May 2009
Article

Configurations of Extremal Even Unimodular Lattices

We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. View Details

Keywords: Mathematical Methods

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A Correspondence Note on Myerson's 'Irrationality via Well-ordering'

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Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)

By: Scott Duke Kominers and Zachary Abel

We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1. View Details

Keywords: Mathematical Methods

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Leonard Bernstein's Doodles: Reading Outside the Lines at the Library of Congress

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2009
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On Universal Binary Hermitian Forms

Earnest and Khosravani, Iwabuchi, and Kim and Park recently gave a complete classification of the universal binary Hermitian forms. We give a unified proof of the universalities of these Hermitian forms, relying upon Ramanujan's list of universal quadratic forms... View Details

Keywords: Mathematical Methods

2024
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Jerry R. Green (1946-)

By: Eddie Dekel, John Geanakoplos and Scott Duke Kominers

Jerry Green has a deep and long-standing connection to Harvard University, and in particular with its Economics Department. This paper begins by reviewing his intellectual background, and then turns to exploring how he has influenced scholars through his wide-ranging... View Details

Keywords: Economics; Microeconomics; Theory; History; Game Theory; Decision Choices and Conditions; Education Industry; North America; United States; Cambridge; Massachusetts; Boston