LLL reduction and a conjecture of Gunnells

Doud, Darrin; Ricks, Russell

doi:10.1090/S0002-9939-09-10131-4

LLL reduction and a conjecture of Gunnells
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by Darrin Doud and Russell Ricks PDF

Proc. Amer. Math. Soc. 138 (2010), 409-415 Request permission

Abstract:

Paul Gunnells has developed an algorithm for computing actions of Hecke operators on arithmetic cohomology below the cohomological dimension. One version of his algorithm uses a conjecture concerning LLL-reduced matrices. We prove this conjecture for dimensions 2 through 5 and disprove it for all higher dimensions.

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