Kevin Ford's Reprints and Preprints



Reviews of all papers , from MathSciNet


Research Papers (in print)

  1. Some infinite series identities , Proc. of the Amer. Math. Soc. 119 (1993), no. 3, 1019-1020. PS file
  2. The representation on numbers as sums of unlike powers, J. London Math. Soc. (2) 51 (1995), 14-26. DVI file (55K) , PS file (239K) .
  3. The representation on numbers as sums of unlike powers, II , J. Amer. Math. Soc. 9 (1996), 919-940. DVI file (94K) , PDF file (279K) ; Addendum and Corrigendum (PDF file, 132K) , J. American Math. Soc. 12 (1999), 1213.
  4. New estimates for mean values of Weyl sums, International Mathematical Research Notices 1995, 155-171. PS file
  5. Sums and products from a finite set of real numbers , The Ramanujan Journal 2, no. 1-2, (1998), 59-66. PS file
  6. The distribution of totients , The Ramanujan Journal 2, no. 1-2. (1998), 67-151. PS file (750K) , DVI file (357K) , PDF file (734K) .
  7. On two conjecture of Sierpinski concerning the arithmetic functions σ and φ , with S. Konyagin. Number Theory in Progress (Zakopane, Poland 1997), de Gruyter (1999), 795-803. PS file (170K) , DVI file (32K) , PDF file (167K) .
  8. Residue classes free of values of Euler's function , with S. Konyagin and C. Pomerance. Number Theory in Progress (Zakopane, Poland 1997), de Gruyter (1999), 805-812. PS file , PDF file ,
  9. The normal behavior of the Smarandache function , Smarandache Notions J. 10, no. 1-2-3. (1999), 81--86. DVI format, PDF format. ERRATA: The constants appearing in Theorem 1 and Corollary 3 are incorrect. The factors 1+log 2 should be replaced by 2. The main error is on page 4, equation (2). The second argument to the second ψ term should be p , not q (Thanks to A. Ivic for discovering this).
  10. The number of solutions of φ(x)=m , Annals of Math. 150 (1999), 283--311. DVI file (136K) , PDF file (299K) .
  11. The Brun-Hooley sieve , with H. Halberstam. J. Number Theory 81 (2000), 335-350. PDF file
  12. Waring's problem with polynomial summands , J. London Math. Soc. (2) 61 (2000), 671-680. DVI file, PDF file.
  13. On an irreducibility theorem of A. Schinzel associated with coverings of the integers , with M. Filaseta and S. Konyagin. Illinois J. of Math. 44 (2000), 633-643. PDF file
  14. Zeros of Dirichlet L-functions near the real axis and Chebyshev's bias , with C. Bays, R. Hudson and M. Rubinstein. J. Number Theory 87 (2001), 54-76. PDF File
  15. An explicit sieve bound and small values of σ(φ(m)) , Periodica Math. Hung. 43 (1-2), (2001), 15-29. PDF File
  16. Sign changes in πq,a(x) - πq,b(x) , with R. Hudson, Acta Arithmetica 100 (2001), 297-314.ct PDF File
  17. The prime number race and zeros of Dirichlet L-functions off the critical line , with S. Konyagin, Duke Math. J. 113 (2002), 313-330. PDF File , DVI File .
  18. Vinogradov's integral and bounds for the Riemann zeta function , Proc. London Math. Soc. 85 (2002), 565-633. PDF File . List of errata .
  19. Zero-free regions for the Riemann zeta function , Number Theory for the Millenium (Urbana, IL, 2000), vol. II (2002), 25-56. PDF File
  20. Maximal collections of intersecting arithmetic progressions , Combinatorica 23 (2) (2003), 263-281. PDF File
  21. The jumping champions of the Farey series , with C. Cobeli and A. Zaharescu; Acta Arithmetica 110 (2003), no. 4, 259--274 PDF file
  22. The prime number race and zeros of Dirichlet L-functions off the critical line, II , with S. Konyagin, Proceedings of the session in analytic number theory and Diophantine equations (Bonn, January--June 2002), Bonner Mathematische Schiften, Nr. 360 (D. R. Heath-Brown, B. Z. Moroz, editors), Bonn, Germany, 2003, 40 pages. PDF file
  23. A strong form of a problem of R. L. Graham , Canadian Math. Bulletin 47 (3), (2004), 358-368. PDF FILE
  24. On Bombieri's asymptotic sieve , Trans. Amer. Math. Soc. 357 (2005), 1663-1674. Electronic versions of the paper (from the AMS web site)
  25. Cycling via common divisors; Solution of Problem 11019(b), with S. Konyagin, Amer. Math. Monthly 112 (2005), 277-278.
  26. On the distribution of imaginary parts of zeros of the Riemann zeta function , with A. Zaharescu, J. reine angew. Math. 579 (2005), 145-158. PDF file (14 pages)
  27. On the maximal difference between an element and its inverse in residue rings , with M. R. Khan, I. E. Shparlinski and C. L. Yankov, Proc. Amer. Math. Soc. 133 (2005), 3463-3468. PDF file
  28. Values of the Euler function in various sequences , with W. D. Banks, F. Luca, F. Pappalardi and I. E. Shparlinski, Monatshefte Math. 146 (2005), 1-19. PDF file
  29. Sieving by large integers, and covering systems of congruences , with M. Filaseta, S. Konyagin, C. Pomerance and G. Yu, J. Amer. Math. Soc. , 20 (2007), 495-517. PDF file
  30. The distribution of integers with at least two divisors in a short interval , with G. Tenenbaum, Quart. J. Math. Oxford 58 (2007), 187-201. PDF file
  31. Generalized Smirnov statistics and the distribution of prime factors , Funct. Approx. Comm. Math. 37.1 (2007), 119-129. PDF file (10 pages).
  32. Localized large sums of random variables , with G. Tenenbaum, Stat. Prob. Letters 78 (2008), 84-89. PDF file
  33. Sharp Probability estimates for generalized Smirnov statistics Monatshefte Math. 153 (2008), 205-216. PDF file
  34. The distribution of integers with a divisor in a given interval , Annals of Math. (2) 168 (2008), 367-433. PDF file (26 JUNE 2008 FINAL VERSION)
  35. Integers with a divisor in (y,2y] , Anatomy of Integers (Jean-Marie De Koninck, Andrew Granville, and Florian Luca, eds), CRM Proc. and Lect. Notes 46 , Amer. Math. Soc., Providence, RI, 2008, 65-81. PDF file, (JULY 17, 2007 REVISION).

Expository/Survey/Announcement Papers

  1. The distribution of totients, ERA Amer. Math. Soc. , 4 (1998), 27-34. PS, DVI or TeX source.
  2. Chebyshev's conjecture and the prime number race , with S. Konyagin, Modern Problems of Number Theory and its Applications; Topical Problems Part II (Tula, Russia, 2001). (2002), 67-91. PDF File
  3. Recent progress on the estimation of Weyl sums , Modern Problems of Number Theory and its Applications; Topical Problems Part II (Tula, Russia, 2001). (2002), 48-66. PDF File
  4. From Kolmogorov's theorem on empirical distribution to number theory , appeared in the book "Kolmogorov's legacy in mathematics", eds. E. Charpentier et al., Editions Belin (Paris), 2004, 111-120. The printed version is in French. PDF file of English original (8 pages). See below for an updated version (appeared in the English version of the book).
  5. From Kolmogorov's theorem on empirical distribution to number theory . Appeared in the book Kolmogorov's heritage in mathematics (English edition) , Editions Belin/Springer, 2007, 97-108. Updated version (with sketch of a different proof of the main result). PDF file (13 pages).

Preprints (submitted, not yet in print)

  1. On curves over finite fields with Jacobians of small exponent , with I. E. Shparlinski, Int. J. Number Theory (to appear), PDF file (10 pages). (12 MAR. 2007 REVISION).
  2. Diophantine approximation with arithmetic functions , with E. Alkan and A. Zaharescu, Trans. Amer. Math. Soc. (to appear) PDF file (15 pages), (9 May 2008 REVISION)
  3. Sharp probability estimates for random walks with barriers , Prob. Th. Rel. Fields (to appear), PDF file (18 pages), (2 May 2008 REVISION)
  4. Generalized Euler constants , with H. G. Diamond, Math. Proc. Cambridge Phil. Soc. (to appear), PDF file (13 pages). (25 February 2008 REVISION)
  5. Divisors of the Euler and Carmichael functions , with Y. Hu, Acta Arithmetica (to appear), PDF file (11 pages). (3 OCTOBER 2007 REVISION)
  6. On the largest prime factor of the Mersenne numbers , with F. Luca and I. E. Shparlinski, submitted April 2007, PDF file (11 pages).
  7. On the distribution of imaginary parts of zeros of the Riemann zeta function, II , with K. Soundararajan and A. Zaharescu, submitted. PDF file (16 pages).
  8. Diophantine approximation with arithmetic functions, II , with E. Alkan and A. Zaharescu, submitted. PDF file (8 pages).

Last Updated: 5 July 2008