Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-16T11:46:41.364Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Theorem of Bombieri, Friedlander, and Iwaniec

Published online by Cambridge University Press:  20 November 2018

Daniel Fiorilli
Daniel Fiorilli*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, Montréal, QC H3C 3J7 email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this article, we show to what extent one can improve a theorem of Bombieri, Friedlander and Iwaniec by using Hooley's variant of the divisor switching technique. We also give an application of the theorem in question, which is a Bombieri-Vinogradov type theorem for the Tichmarsh divisor problem in arithmetic progressions.

Keywords

11N13primes in arithmetic progressionsTitchmarsh divisor problem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 5 , 01 October 2012 , pp. 1019 - 1035
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Bombieri, E., Friedlander, J. B., and Iwaniec, H., Primes in arithmetic progressions to large moduli. Acta Math. 156(1986), no. 3–4, 203–251. http://dx.doi.org/10.1007/BF02399204 Google Scholar
[2] Bombieri, E., Primes in arithmetic progressions to large moduli. II. Math. Ann. 277(1987), no. 3, 361–393. http://dx.doi.org/10.1007/BF01458321 Google Scholar
[3] Bombieri, E., Primes in arithmetic progressions to large moduli. III. J. Amer. Math. Soc. 2(1989), no. 2, 215–224. http://dx.doi.org/10.1090/S0894-0347-1989-0976723-6 Google Scholar
[4] Felix, A. T., Generalizing the Titchmarsh divisor problem. Int. Number Theory, J., to appear. http://dx.doi.org/10.1142/S1793042112500340 Google Scholar
[5] Fiorilli, D., Residue classes containing an unexpected number of primes. arxiv:1009.2699.Google Scholar
[6] Fouvry, É., Autour du théorème de Bombieri-Vinogradov. Acta Math. 152(1984), no. 3–4, 219–244. http://dx.doi.org/10.1007/BF02392198 Google Scholar
[7] Fouvry, É., Autour du théorème de Bombieri-Vinogradov. II. Ann. Sci. È cole Norm. Sup. (4) 20(1987), no. 4, 617–640.Google Scholar
[8] Fouvry, É., Sur le problème des diviseurs de Titchmarsh. J. Reine Angew. Math. 357(1985), 51–76. http://dx.doi.org/10.1515/crll.1985.357.51 Google Scholar
[9] Fouvry, É. and Iwaniec, H., On a theorem of Bombieri-Vinogradov type. Mathematika 27(1980), no. 2, 135–152 (1981). http://dx.doi.org/10.1112/S0025579300010032 Google Scholar
[10] Fouvry, É. and Iwaniec, H., Primes in arithmetic progressions. Acta Arith. 42(1983), no. 2, 197–218.Google Scholar
[11] Friedlander, J. B., Granville, A., Hildebrand, A., and Maier, H., Oscillation theorems for primes in arithmetic progressions and for sifting functions. J. Amer. Math. Soc. 4(1991), no. 1, 25–86. http://dx.doi.org/10.1090/S0894-0347-1991-1080647-5 Google Scholar
[12] Goldston, D. A., Pintz, J., and Yildirim, C. Y., Primes in tuples. I. Ann. of Math. (2) 170(2009), no. 2, 819–862. http://dx.doi.org/10.4007/annals.2009.170.819 Google Scholar
[13] Hooley, C., On the Barban-Davenport-Halberstam theorem. I. Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, III. J. Reine Angew. Math. 274/275(1975), 206–223. http://dx.doi.org/10.1515/crll.1975.274-275.206Google Scholar