3 problems

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The density conjecture for quaternion algebras realizing the $E_8$ lattice
Let $\mathcal{D}_2$ denote the set of discriminants under consideration, and consider quaternion algebras $B=\left(\frac{-1,-1}{F}\right)$ over number fields $F$ whose maximal orde…
Conjectureopennumber-fields quaternion-algebras unimodular-latticesarXiv posted 2 days ago
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The cutoff conjecture for representations by unimodular lattices
Cutoff conjecture. If
Conjectureopenquadratic-forms representation-theory unimodular-latticesarXiv posted 2 days ago
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Montague's conjecture on the twisted construction of the Niemeier lattice with root system $D_{24}$
Let $C$ be a self-dual ternary code of length $24$ containing the all-one vector. The twisted construction associates to $C$ the unimodular neighbor … where … and…
Conjectureopenniemeier-lattices self-dual-codes unimodular-latticesarXiv posted 2 days ago

The density conjecture for quaternion algebras realizing the E8E_8E8​ lattice