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LLL reduction and a conjecture of Gunnells

Author(s): Darrin Doud; Russell Ricks
Journal: Proc. Amer. Math. Soc. 138 (2010), 409-415.
MSC (2000): Primary 11H55; Secondary 11F75
Posted: September 17, 2009
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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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Additional Information:

Darrin Doud
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: doud@math.byu.edu

Russell Ricks
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: russellricks@byu.edu

DOI: 10.1090/S0002-9939-09-10131-4
PII: S 0002-9939(09)10131-4
Keywords: LLL-reduced lattices
Received by editor(s): December 31, 2008
Posted: September 17, 2009
Communicated by: Ken Ono
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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