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On primitive roots of tori: The case of function fields

✍ Scribed by Yen-Mei J. Chen; Yoshiyuki Kitaoka; Jing Yu

Book ID
118296814
Publisher
Springer-Verlag
Year
2003
Tongue
French
Weight
184 KB
Volume
243
Category
Article
ISSN
0025-5874

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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 Β₯ 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 modu

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Let N g =[g n : 1 n N], where g is a primitive root modulo an odd prime p, and let f g (m, H) denote the number of elements of N g that lie in the interval (m, m+H], where 1 m p. H. Montgomery calculated the asymptotic size of the second moment of f g (m, H) about its mean for a certain range of the