Normal regular Hermitian lattices over imaginary quadratic fields
Acta Arithmetica, Tome 179 (2017) no. 1, pp. 37-53
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
A positive definite Hermitian lattice over an imaginary quadratic field is called regular if it represents every number represented by its genus. It is called universal if it represents all positive integers. We show that every primitive normal regular integral lattice over a fixed imaginary quadratic field is actually universal if and only if the field discriminant is not 4, 8, 11, 23 and is prime to $3\cdot 5\cdot 7$.
Keywords:
positive definite hermitian lattice imaginary quadratic field called regular represents every number represented its genus called universal represents positive integers every primitive normal regular integral lattice fixed imaginary quadratic field actually universal imaginary quadratic field only field discriminant prime cdot cdot
Affiliations des auteurs :
Poo-Sung Park 1
@article{10_4064_aa8582_10_2016,
author = {Poo-Sung Park},
title = {Normal regular {Hermitian} lattices over imaginary quadratic fields},
journal = {Acta Arithmetica},
pages = {37--53},
year = {2017},
volume = {179},
number = {1},
doi = {10.4064/aa8582-10-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8582-10-2016/}
}
Poo-Sung Park. Normal regular Hermitian lattices over imaginary quadratic fields. Acta Arithmetica, Tome 179 (2017) no. 1, pp. 37-53. doi: 10.4064/aa8582-10-2016
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