The difference between consecutive primes in an arithmetic progression

Quarterly Journal of Mathematics

Volumn 53, Issue 4, 2002, Pages 479-501

  Kumchev, A ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036935964     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmath/53.4.479     Document Type: Article

References (20)

1. R. C. Baker and G. Harman, The difference between consecutive primes, Proc. London Math. Soc. 72 (1996), 261-280.
2. 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, London Mathematical Society Lecture Notes, 237, Cambridge University Press, Cambridge, (1997), 1-54.
3. R. C. Baker, G. Harman, and J. Pintz, The difference between consecutive primes II, Proc. London Math. Soc. 83 (2001), 532-562.
4. A. Fujii, P. X. Gallagher, and H. L. Montgomery, Some hybrid bounds for character sums and Dirichlet L-functions, Topics in Number Theory, Colloq. Math. Soc. Janos Bolyai, 13, North-Holland, Amsterdam, (1976), 41-57.
5. H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974.
6. G. Harman, A. Kumchev, and P. A. Lewis, The distribution of prime ideals of imaginary quadratic fields, Trans. Amer. Math. Soc., to appear.
7. D. R. Heath-Brown, The number of primes in a short interval, J. Reine Angew. Math. 389 (1988), 22-63.
8. G. Hoheisel, Primzahlprobleme in der analysis, Sitz. Preuss. Akad. Wiss. 2 (1930), 1-13.
9. M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170.
10. M. N. Huxley and H. Iwaniec, Bombieri's theorem in short intervals, Mathematika 22 (1975), 188-194.
11. M. Jutila, A statistical density theorem for L-functions with applications, Acta Arith. 16 (1969), 207-216.
12. P. A. Lewis, Finding information about Gaussian primes using sieves, Ph. D. Thesis, Cardiff University, 2001.
13. H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Mathematics, 227, Springer, Berlin, 1971.
14. Y. Motohashi, On a mean value theorem for the remainder term in the prime number theorem for short arithmetic progressions, Proc. Japan Acad. Ser. A Math. Sci. 47 (1971), 653-657.
15. A. Perelli, J. Pintz, and S. Salerno, Bombieri's theorem in short intervals, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 11 (1984), 529-539.
16. A. Perelli, J. Pintz, and S. Salerno, Bombieri's theorem in short intervals II, Invent. Math. 79 (1985), 1-9.
17. H. Rademacher, On the Phragmen-Lindelöf theorem and some applications, Math. Z. 72 (1959/60), 192-204.
18. S. J. Ricci, Mean-value theorems for primes in short intervals, Proc. London Math. Soc. 37 (1978), 230-242.
19. N. M. Timofeev, Distribution in the mean of arithmetic functions in short intervals in arithmetic progressions, Math. USSR-Izv. 30 (1988), 315-335.
20. N. Watt, Kloosterman sums and a mean value for Dirichlet polynomials, J. Number Theory 53 (1995), 179-210.