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A Comment on the Hadamard Conjecture

✍ Scribed by Warwick de Launey; Daniel M. Gordon

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 88 KB
Volume: 95
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3155

No coin nor oath required. For personal study only.

✦ Synopsis

Fix n. Let r(n) denote the largest number r for which there is an r_n (1, &1)matrix H satisfying the matrix equation HH =nI r . The Hadamard conjecture states that for n divisible by 4 we have r(n)=n. Let =>0. In this paper, we show that the Extended Riemann Hypothesis and recent results on the asymptotic existence of Hadamard matrices imply that for n sufficiently large r(n)>( 12 &=) n.

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