On Primitive Roots of One-Dimensional Tori

✍ Scribed by Yen-Mei J Chen

• Book ID: 102600779
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 131 KB
• Volume: 93
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2001.2706

✦ Synopsis

We exploit an analogue of Artin's primitive roots conjecture for one-dimensional tori over Q. Let T be a one-dimensional torus over Q, and let P ¥ T(Q) be a nontorsion point. Under Generalized Riemann Hypothesis, we derive an explicit density formula for the set of rational primes a such that P modulo a generates T(F a ).