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Darrin Doud

214 TMCB Department of Mathematics Brigham Young University Provo, UT 84602

phone: (801)422-1204 fax: (801)422-0504 e-mail:

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LLL reductions and a conjecture of Gunnells

with Russell Ricks

Proceedings of the AMS 138 (2010), 409-415.

Abstract: Paul Gunnells has developed an algorithm for computing actions of Hecke operators on arithmetic cohomology below the cohomological dimension. His algorithm uses a conjecture concerning LLL-reduced matrices. We prove this conjecture in dimensions two through five and disprove it in all higher dimensions.

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Programs Used

GP Code for the dimension four case.

GP Code for the dimension five case.

GP Code for Gram-Schmidt reduction and testing LLL conditions.