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Ankeny–Artin–Chowla Conjecture and Continued Fraction Expansion

✍ Scribed by Ryūta Hashimoto

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 115 KB
Volume: 90
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2652

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✦ Synopsis

For any prime p congruent to 1 modulo 4, let (t+u -p)Â2 be the fundamental unit of Q(p). Then Ankeny, Artin, and Chowla conjectured that u is not divisible by p. In this paper, we investigate a certain relation between the conjecture and the continued fraction expansion of (1+p)Â2. Consequently, we prove that the conjecture is true if p is not ``small'' in some sense.

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