Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the largest prime factors of consecutive integers in short intervals


Author: Zhiwei Wang
Journal: Proc. Amer. Math. Soc. 145 (2017), 3211-3220
MSC (2010): Primary 11N36, 11-XX, 11Nxx
DOI: https://doi.org/10.1090/proc/13459
Published electronically: January 31, 2017
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Régis de la Bretèche, Carl Pomerance, and Gérald Tenenbaum, Products of ratios of consecutive integers, Ramanujan J. 9 (2005), no. 1-2, 131-138. MR 2166384, https://doi.org/10.1007/s11139-005-0831-7
  • [2] K. Dickman,
    On the frequency of numbers containing prime factors of a certain relative magnitude,
    Ark. Mat. Astr. Fys. 22(A10) (1930), 1-14.
  • [3] Paul Erdős and Carl Pomerance, On the largest prime factors of $ n$ and $ n+1$, Aequationes Math. 17 (1978), no. 2-3, 311-321. MR 0480303
  • [4] Adolf Hildebrand, On the number of positive integers $ \leq x$ and free of prime factors $ >y$, J. Number Theory 22 (1986), no. 3, 289-307. MR 831874, https://doi.org/10.1016/0022-314X(86)90013-2
  • [5] Henryk Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. MR 598883
  • [6] Henryk Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), no. 2, 171-202. MR 581917
  • [7] Jean-Louis Nicolas, Nombres hautement composés, Acta Arith. 49 (1988), no. 4, 395-412 (French). MR 937935
  • [8] A. Perelli, J. Pintz, and S. Salerno, Bombieri's theorem in short intervals, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 4, 529-539. MR 808422
  • [9] N. M. Timofeev, Distribution of arithmetic functions in short intervals in the mean with respect to progressions, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), no. 2, 341-362, 447 (Russian); English transl., Math. USSR-Izv. 30 (1988), no. 2, 315-335. MR 897001
  • [10] J. Wu, Théorèmes généralisés de Bombieri-Vinogradov dans les petits intervalles, Quart. J. Math. Oxford Ser. (2) 44 (1993), no. 173, 109-128 (French). MR 1206205, https://doi.org/10.1093/qmath/44.1.109

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11N36, 11-XX, 11Nxx

Retrieve articles in all journals with MSC (2010): 11N36, 11-XX, 11Nxx


Additional Information

Zhiwei Wang
Affiliation: Institut Élie Cartan, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre-lès-Nancy Cedex, France
Email: zhiwei.wang@univ-lorraine.fr

DOI: https://doi.org/10.1090/proc/13459
Received by editor(s): May 13, 2016
Received by editor(s) in revised form: August 29, 2016
Published electronically: January 31, 2017
Additional Notes: The author was supported by the China Scholarship Council
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society