Similar sublattices of the root lattice A(4)

Baake M, Heuer M, Moody RV (2008)
JOURNAL OF ALGEBRA 320(4): 1391-1408.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Baake, MichaelUniBi; Heuer, Manuela; Moody, Robert V.
Abstract / Bemerkung
Similar sublattices of the root lattice A(4) are possible [J.H. Conway, E.M. Rains, N.J.A. Sloane, On the existence of similar sublattices, Can. J. Math. 51 (1999) 1300-1306] for each index that is the square of a non-zero integer of the form m(2) + mn - n(2). Here, we add a constructive approach, based on the arithmetic of the quaternion algebra H(Q(root 5)) and the existence of a particular involution of the second kind, which also provides the actual sublattices and the number of different solutions for a given index. The corresponding Dirichlet series generating function is closely related to the zeta function of the icosian ring. (c) 2008 Michael Baake. Published by Elsevier Inc. All rights reserved.
Stichworte
icosian ring; similar sublattices; zeta function
Erscheinungsjahr
2008
Zeitschriftentitel
JOURNAL OF ALGEBRA
Band
320
Ausgabe
4
Seite(n)
1391-1408
ISSN
0021-8693
Page URI
https://pub.uni-bielefeld.de/record/1587018

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Baake M, Heuer M, Moody RV. Similar sublattices of the root lattice A(4). JOURNAL OF ALGEBRA. 2008;320(4):1391-1408.
Baake, M., Heuer, M., & Moody, R. V. (2008). Similar sublattices of the root lattice A(4). JOURNAL OF ALGEBRA, 320(4), 1391-1408. https://doi.org/10.1016/j.jalgebra.2008.04.021
Baake, M., Heuer, M., and Moody, R. V. (2008). Similar sublattices of the root lattice A(4). JOURNAL OF ALGEBRA 320, 1391-1408.
Baake, M., Heuer, M., & Moody, R.V., 2008. Similar sublattices of the root lattice A(4). JOURNAL OF ALGEBRA, 320(4), p 1391-1408.
M. Baake, M. Heuer, and R.V. Moody, “Similar sublattices of the root lattice A(4)”, JOURNAL OF ALGEBRA, vol. 320, 2008, pp. 1391-1408.
Baake, M., Heuer, M., Moody, R.V.: Similar sublattices of the root lattice A(4). JOURNAL OF ALGEBRA. 320, 1391-1408 (2008).
Baake, Michael, Heuer, Manuela, and Moody, Robert V. “Similar sublattices of the root lattice A(4)”. JOURNAL OF ALGEBRA 320.4 (2008): 1391-1408.

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