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On the Distribution of Small Powers of a Primitive Root

✍ Scribed by C.I Cobeli; S.M Gonek; A Zaharescu

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
124 KB
Volume
88
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 parameters N and H and asked to what extent this range could be increased if one were to average over all the primitive roots (mod p). We address this question as well as the related one of averaging over the prime p.

2001 Academic Press

1. INTRODUCTION AND STATEMENT OF RESULTS

Let g be a primitive root modulo an odd prime p and let

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