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On the Representation of Integers by the Lorentzian Quadratic Form

✍ Scribed by John G. Ratcliffe; Steven T. Tschantz

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 413 KB
Volume: 150
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3129

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✦ Synopsis

In this paper, we establish an asymptotic formula, for large radius r, for the number of representations of a nonzero integer k by the Lorentzian quadratic form x 2 1 +x 2 2 + } } } +x 2 n &x 2 n+1 that are contained in the ball of radius r centered at the origin in Euclidean (n+1)-space. 1997 Academic Press s(n, k, r)t

Vol(S n&1 ) (n&1) 2 (n&1)Â2 $(n, k) r n&1 as r Ä .

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