Representations of Positive Definite Quadratic Forms with Congruence and Primitive Conditions

✍ Scribed by M. Jochner; Y. Kitaoka

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 567 KB
• Volume: 48
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1994.1055

✦ Synopsis

Let (M) be a positive definite (Z)-lattice of rank (m \geqslant 2 n+3) and let (T) be a finite set of primes containing 2 and those primes (p) for which (M_{p}) is not unimodular. If (N) is a lattice of rank (n) which is locally represented by (M) and if (\min (N)) is sufficiently large then there exists a representation (f: N \rightarrow M) so that (f) approximates given local representations at (T) and so that (f\left(N_{p}\right)) is primitive in (M_{p}) for all primes (p \notin T \cup{q}) where (q) is any fixed prime not in (T). 1994 Academic Press, Inc.