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. Note: the PDF version here is the updated 2012 version, with various corrections and simplifications to the original paper.
  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. Note: This paper was neither submitted to, nor refereed by, this journal. 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 111 (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.
  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.
  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.
  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.
  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.
  31. Generalized Smirnov statistics and the distribution of prime factors , Funct. Approx. Comm. Math. 37.1 (2007), 119-129.
  32. Localized large sums of random variables , with G. Tenenbaum, Stat. Prob. Letters 78 (2008), 84-89.
  33. Sharp Probability estimates for generalized Smirnov statistics , Monatshefte Math. 153 (2008), 205-216.
  34. The distribution of integers with a divisor in a given interval , Annals of Math. (2) 168 (2008), 367-433.
  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, 65-80. Updated, simplified version (2012)
  36. Generalized Euler constants , with H. G. Diamond, Math. Proc. Cambridge Phil. Soc. 145 (2008), 27-41.
  37. Divisors of the Euler and Carmichael functions, with Y. Hu, Acta Arithmetica 133 (2008), 199-208.
  38. On curves over finite fields with Jacobians of small exponent, with I. E. Shparlinski, Int. J. Number Theory 4 (2008), 819-826.
  39. On the distribution of imaginary parts of zeros of the Riemann zeta function, II , with K. Soundararajan and A. Zaharescu, Math. Annalen 343 (2009), 487-505.
  40. Diophantine approximation with arithmetic functions , with E. Alkan and A. Zaharescu, Trans. Amer. Math. Soc. 361 (2009), 2263-2275.
  41. On the largest prime factor of the Mersenne numbers , with F. Luca and I. E. Shparlinski, Bull. Austr. Math. Soc. 79 (2009), 455-463.
  42. Sharp probability estimates for random walks with barriers , Prob. Th. Rel. Fields 145 (2009), 269-283.
  43. Diophantine approximation with arithmetic functions, II , with E. Alkan and A. Zaharescu, Bull. London Math. Soc. 41 (2009), 676-682.
  44. Common values of the arithmetic functions φ and σ , with Florian Luca and Carl Pomerance, Bull. London Math. Soc. 42 (2010), 478-488.
  45. Geometric Properties of Points on Modular Hyperbolas , with Mizan Khan and Igor Shparlinski, Proc. Amer. Math. Soc. 138 (2010), 4177-4185.
  46. On the divisibility of Fermat quotients , with J. Bourgain, S. V. Konyagin and I. E. Shparlinski, Michigan Math. J. 59 (2010), 313-328.
  47. Prime chains and Pratt trees , with Sergei V. Konyagin and Florian Luca, Geom. Funct. Anal. 20 (2010), 1231-1258.
  48. Chebyshev's bias for products of two primes , with Jason Sneed, Experim. Math. 19 (2010), 385-398.
  49. The number of solutions of λ(x)=n , with Florian Luca, INTEGERS (Proceedings of the INTEGERS conference honoring Melvyn Nathanson and Carl Pomerance) 11A (2011), Article 9.
  50. Explicit constructions of RIP matrices and related problems , with J. Bourgain, S. J. Dilworth, S. Konyagin and D. Kutzarova, Duke Math. J. 159 (2011), 145-185.
  51. Breaking the k2 barrier for explicit RIP matrices , with J. Bourgain, S. J. Dilworth, S. Konyagin and D. Kutzarova, Proceedings of the 43rd Symposium on the Theory of Computing (STOC '11) (2011), 637-644.
  52. On common values of φ(n) and σ(m), I . with Paul Pollack, Acta Math. Hungarica 133 (2011), 251-271.
  53. A problem of Ramanujan, Erdos and Katai on the iterated divisor function , with Y. Buttkewicz, C. Elsholtz and J.-C. Schlage-Puchta, International Mathematical Research Notices 2012 , 4051-4061.
  54. On common values of φ(n) and σ(m), II . with Paul Pollack, Algebra and Number Theory 6 (2012), no. 8, 1669-1696.
  55. On groups with perfect order subsets , with Sergei Konyagin and Florian Luca. Moscow J. Comb. Number Th. 2 (2012), 297-312.
  56. Poisson-Dirichlet branching random walks . with Louigi Addario-Berry, Ann. Appl. Prob. 23 , (1) (2013), 283-307.
  57. On square values of the product of the Euler totient and sum of divisors functions . with Kevin Broughan and Florian Luca, Colloq. Math. 130 (2013), 127-137.
  58. On non-intersecting arithmetic progressions , with Régis de la Bretèche and Joseph Vandehey, Acta Arithmetica 157 (2013), 381-392.
  59. The prime number race and zeros of L-functions off the critical line. III. with Sergei Konyagin and Youness Lamzouri, Quart. J. Math. Oxford 64 (2013), 1091-1098.
  60. Values of the Euler φ-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields , with Florian Luca and Pieter Moree, Math. Comp. 83 (2014), no. 287, 1447-1476.
  61. Sieving very thin sets of primes, and Pratt trees with missing primes . International Mathematical Research Notices 2014 (2014), 2955-2971.

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.
  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.
  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 Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing , with Trevor D. Wooley, Acta Mathematica, to appear. 33 pages. (18 Dec 2013 revision)
  2. Unnormalized differences between zeros of L-functions , with Alexandru Zaharescu, Compositio Math. (to appear). 20 pages. (May 2014 revision)
  3. The image of Carmichael's λ-function , with Florian Luca and Carl Pomerance, submitted. 15 pages. 27-AUG-2014 Revision.
  4. Large gaps between consecutive prime numbers , with Ben Green, Sergei Konyagin and Terence Tao, 32 pages.

Last Updated: 27 August 2014