On generalizing Artin's conjecture on primitive roots to composite moduli

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 556, 2003, Pages 205-224

  Li, Shuguang ^a   Pomerance, Carl ^b  

^a UNIVERSITY OF HAWAII AT HILO   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037248579     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2003.022     Document Type: Article

References (16)

1. P. Erdos and C. Pomerance, On the normal number of prime factors of φ(n), Rocky Mountain J. Math. 15 (1985), 343-352. (Corrigendum in P. Erdos, A. Granville, C. Pomerance and C. Spiro, On the normal behavior of the iterates of some arithmetic functions, in: Analytic Number Theory, Proc. Bateman Conf., Birkhäuser, Boston (1990), 165-204.)
2. P. Erdos, C. Pomerance, and E. Schmutz, Carmichael's lambda function, Acta Arith. 58 (1991), 363-385.
3. J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Period of the power generator and small values of Carmichael's function, Math. Comp. 70 (2001), 1591-1605.
4. H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London 1974.
5. C. Hooley, On Artin's conjecture, J. reine angew. Math. 225 (1967), 209-220.
6. P. Kurlberg, On the order of unimodular matrices modulo integers, preprint, http://www.math.chalmers.se/̃kurlberg/.
7. J. C. Lagarias and A. M. Odlyzko, Effective versions of the Chebotarev density theorem, in: Algebraic Number Fields: L-functions and Galois properties, Proc. Sympos. Univ. Durham, Durham 1975, A. Fröhlich, ed., Academic Press, London (1977). 409-464.
8. S. Li, On the number of elements with maximal order in the multiplicative group modulo n, Acta Arith. 86 (1998), 113-132.
9. S. Li, On extending Artin's conjecture to composite moduli, Mathematika 46 (1999), 373-390.
10. S. Li, Artin's conjecture on average for composite moduli, J. Number Th. 84 (2000), 93-118.
11. G. Martin, The least prime primitive root and the shifted sieve, Acta Arith. 80 (1997), 277-288.
12. M. R. Murty, M. Rosen, and J. H. Silverman, Variations on a theme of Romanoff, Internat. J. Math. 7 (1996), 373-391.
13. M. R. Murty and F. Saidak, Non-abelian generalizations of the Erdos-Kac theorem, preprint 2001.
14. C. Pomerance, On the distribution of amicable numbers, J. reine angew. Math. 293/294 (1977), 217-222.
15. C. Pomerance, On primitive divisors of Mersenne numbers, Acta Arith. 46 (1986), 355-367.
16. F. Saidak, Non-abelian generalizations of the Erdos-Kac theorem, Ph.D. Thesis, Queen's University, Kingston, Canada 2001.