Document Zbl 0538.10027

An application of Siegel’s formula over quaternion orders. (English) Zbl 0538.10027

Mathematika 31, 12-16 (1984).

This paper is concerned with Hermitian forms over a maximal order in a definite quaternion skew field H/\({\mathbb{Q}}\) such that the associated quadratic forms are positive definite and unimodular. An ad hoc proof of Siegel’s formula for the representation of numbers and an application to the existence of forms with large minimum are given. For \(H=(-1,-1)\) the forms are classified up to real dimension 24.

Cited in 7 Documents

MSC:

11H55	Quadratic forms (reduction theory, extreme forms, etc.)
11E12	Quadratic forms over global rings and fields
11F11	Holomorphic modular forms of integral weight
11R52	Quaternion and other division algebras: arithmetic, zeta functions

Keywords:

extremal lattices; Hermitian forms; quaternion skew field; Siegel’s formula; forms with large minimum

Cite Review PDF

Full Text: DOI

References:

[1]	Milnor, Symmetric bilinear forms (1973) · Zbl 0292.10016 · doi:10.1007/978-3-642-88330-9
[2]	DOI: 10.1016/0097-3165(78)90021-3 · Zbl 0397.94013 · doi:10.1016/0097-3165(78)90021-3
[3]	DOI: 10.1007/BF01898782 · Zbl 0078.03801 · doi:10.1007/BF01898782
[4]	Eichler, Quadratischc Formen und orthogonale Gruppen (1952) · doi:10.1007/978-3-662-01212-3
[5]	Serre, A course in arithmetic (1973) · doi:10.1007/978-1-4684-9884-4
[6]	Vigneras, Arithmétique des algèbres de quaternions. Springer Lecture Notes (1980) · doi:10.1007/BFb0091027
[7]	Tits, Finite simple groups pp 303– (1980)
[8]	Sloane, Combinatorial Surveys: Proc. Sixth British Combinatorial Conf pp 117– (1977)
[9]	Weil, Ada Math. 113 pp 1– (1965)

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.