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Currently displaying 1 – 4 of 4

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Configurations of rank- $40 r$ extremal even unimodular lattices ( $r = 1, 2, 3$ )

Scott Duke Kominers; Zachary Abel — 2008

Journal de Théorie des Nombres de Bordeaux

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

Minimal $𝒮$ -universality criteria may vary in size

Noam D. Elkies; Daniel M. Kane; Scott Duke Kominers — 2013

Journal de Théorie des Nombres de Bordeaux

In this note, we give simple examples of sets $𝒮$ of quadratic forms that have minimal $𝒮$ -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.

On universal binary Hermitian forms.

Kominers, Scott Duke — 2009

Integers

On congruence conditions for primality.

Gong, Sherry; Kominers, Scott Duke — 2010

Integers

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