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A Quadratic Analogue of Artin's Conjecture on Primitive Roots

✍ Scribed by Hans Roskam

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 212 KB
Volume: 81
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2470

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✦ Synopsis

Let = be a fundamental unit in a real quadratic field and let S be the set of rational primes p for which = has maximal order modulo p. Under the assumption of the generalized Riemann hypothesis, we show that S has a density $(S)=c } A in the set of all rational primes, where A is Artin's constant and c is a positive rational number.

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