On the number of Carmichael numbers up to x

Bulletin of the London Mathematical Society

Volumn 37, Issue 5, 2005, Pages 641-650

  Harman, Glyn ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26444588658     PISSN: 00246093     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024609305004686     Document Type: Article

References (20)

1. W. R. ALFORD, A. GRANVILLE and C. POMERANCE, 'There are infinitely many Carmichael numbers', Ann. of Math. 140 (1994) 703-722.
2. R. C. BAKER and G. HARMAN, 'Shifted primes without large prime factors', Acta Arith. 83 (1998) 331-361.
3. R. C. BAKER, G. HARMAN and J. PINTZ, 'The exceptional set for Goldbach's problem in short intervals,' Sieve methods, exponential sums and their applications in number theory (ed. G. R. H. Greaves, G. Harman and M. N. Huxley, Cambridge Univ. Press, 1997) 1-54.
4. R. C. BAKER, G. HARMAN and J. PINTZ, 'The difference betweeen consecutive primes, II', Proc. London Math. Soc. (3) 83 (2001) 532-562.
5. H. DAVENPORT, Multiplicative number theory, 2nd edn, revised by H. L. Montgomery (Springer, New York 1980).
6. J. B. FRIEDLANDER, 'Shifted primes without large prime factors', Number theory and applications, NATO Sci. Ser. C Math. Phys. Sci. 265 (ed. R. A. Mollin, Kluwer, Dordrecht, 1989) 393-401.
7. P. X. GALLAGHER, 'A large sieve density estimate near σ = 1', Invent. Math. 16 (1970) 329-339.
8. A. GRANVILLE and C. POMERANCE, 'Two contradictory conjectures concerning Carmichael numbers', Math. Comp. 71 (2002) 883-908.
9. G. HARMAN, 'On the distribution of αp modulo one', J. London Math. Soc. (2) 27 (1983) 9-18.
10. G. HARMAN, 'On the distribution of αp modulo one. II', Proc. London Math. Soc. (3) 72 (1996) 241-260.
11. G. HARMAN, A. KUMCHEV and P. A. LEWIS, 'The distribution of prime ideals of quadratic imaginary fields', Trans. American Math. Soc. 356 (2004) 599-620.
12. G. HARMAN, N. WATT and K. WONG, 'A new mean-value result for Dirichlet L-functions and polynomials', Quart. J. Math. Oxford 55 (2004) 307-324.
13. M. N. HUXLEY, 'Large values of Dirichlet polynomials III', Acta Arith. 26 (1975) 435-444.
14. A. KUMCHEV, 'The difference between consecutive primes in an arithmetic progression', Quart. J. Math. Oxford 53 (2002) 479-501.
15. H. W. LENSTRA, JR. and C. POMERANCE, 'Primality testing with Gaussian periods', preprint, www.math.dartmouth.edu/~carlp/PDF/complexity11.pdf
16. P. A. LEWIS, 'Finding information about Gaussian primes using analytic number theory sieve methods', PhD Thesis, Cardiff, 2002.
17. H. L. MONTGOMERY, Topics in multiplicative number theory, Lecture Notes in Math. 227 (Springer, New York, 1971).
18. H. L. MONTGOMERY and R. C. VAUGHAN, 'The large sieve', Mathematika 20 (1973) 119-134.
19. E. C. TITCHMARSH, Theory of the Riemann Zeta-function, 2nd edn, revised by D. R. Heath-Brown (Clarendon Press, Oxford, 1986).
20. N. WATT, 'Kloosterman sums and a mean value result for Dirichlet polynomials', J. Number Theory 53 (1995) 179-210.