Document Type

Article - preprint


Mathematics (CMC), Mathematics (Pomona)

Publication Date



Hermitian curves, function fields, well-rounded lattices, kissing number, automorphism group


We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of Gerhard Hiss on the factorization of functions with particular divisor support into lines and their inverses.


Final published version can be found at: Böttcher, A., Fukshansky, L., Garcia, S.R., Maharaj, H., Lattices from Hermitian function fields, Journal of Algebra 447 (2016) 560-579.

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© 2015 Elsevier Inc.

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Algebra Commons