Kevin Ford's Reprints and Preprints
Research Papers (in print)
 Some infinite series identities ,
Proc. of the Amer. Math. Soc. 119
(1993), no. 3, 10191020.
PS file
 The representation on numbers as sums of unlike powers,
J. London Math. Soc. (2) 51 (1995), 1426.
DVI file (55K) ,
PS file (239K) .
 The representation on numbers as sums of unlike powers, II
, J. Amer. Math. Soc.
9 (1996), 919940.
DVI file (94K) ,
PDF file (279K) ;
Addendum and Corrigendum (PDF file, 132K)
,
J. American Math. Soc.
12 (1999), 1213.
 New estimates for mean values of Weyl sums,
International Mathematical Research
Notices 1995, 155171.
PS file
 Sums and products from a finite set of real numbers ,
The Ramanujan Journal
2, no. 12, (1998), 5966.
Reprinted in Analytic and elementary number theory: A tribute to
mathematical legend Paul Erdos , (K. Alladi, P. D. T. A. Elliott,
A. Granville and G. Tenenbaum, eds.), Springer, 1998.
PS file

The distribution of totients ,
The Ramanujan Journal
2, no. 12. (1998), 67151.
Reprinted in Analytic and elementary number theory: A tribute to
mathematical legend Paul Erdos , (K. Alladi, P. D. T. A. Elliott,
A. Granville and G. Tenenbaum, eds.), Springer, 1998.
Note: the PDF version here is the updated 2012 version, with various
corrections and simplifications to the original paper.
 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),
795803.
PS file (170K) ,
DVI file (32K) ,
PDF file (167K) .
 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), 805812.
PS file ,
PDF file ,
 The normal behavior of the Smarandache function ,
Smarandache Notions J. 10, no. 123. (1999), 8186.
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).
 The number of solutions of φ(x)=m ,
Annals of Math.
150 (1999), 283311.
DVI file (136K) ,
PDF file (299K) .
 The BrunHooley sieve , with H. Halberstam.
J. Number Theory 81 (2000), 335350.
PDF file
 Waring's problem with polynomial summands ,
J. London Math. Soc.
(2) 61 (2000), 671680.
DVI file,
PDF file.
 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), 633643.
PDF file
 Zeros of Dirichlet Lfunctions near the real axis and
Chebyshev's bias , with C. Bays, R. Hudson and M. Rubinstein.
J. Number Theory 87 (2001), 5476.
PDF File
 An explicit sieve bound and
small values of σ(φ(m)) ,
Periodica Math. Hung. 43
(12), (2001), 1529.
PDF File
 Sign changes in
π_{q,a}(x)  π_{q,b}(x)
, with R. Hudson,
Acta Arithmetica 100 (2001), 297314.ct
PDF File
 The prime number race and zeros of Dirichlet Lfunctions
off the critical line , with S. Konyagin,
Duke Math. J.
113 (2002), 313330.
PDF File ,
DVI File .
 Vinogradov's integral and bounds for the Riemann zeta
function ,
Proc. London Math. Soc. 85 (2002), 565633.
PDF File .
List of errata .
 Zerofree regions for the Riemann zeta function ,
Number Theory for the Millenium (Urbana, IL, 2000), vol. II (2002), 2556.
PDF File
 Maximal collections of intersecting arithmetic progressions
,
Combinatorica 23 (2) (2003), 263281.
PDF File
 The jumping champions of the Farey series ,
with C. Cobeli and A. Zaharescu;
Acta Arithmetica
110 (2003), no. 4, 259274
PDF file
 The prime number race and zeros of Dirichlet Lfunctions
off the critical line, II , with S. Konyagin, Proceedings of
the session in analytic number theory and Diophantine equations (Bonn,
JanuaryJune 2002), Bonner Mathematische Schiften, Nr. 360
(D. R. HeathBrown, B. Z. Moroz, editors), Bonn, Germany, 2003,
40 pages.
PDF file
 A strong form of a problem of R. L. Graham ,
Canadian Math. Bulletin
47 (3), (2004), 358368.
PDF FILE
 On Bombieri's asymptotic sieve ,
Trans. Amer. Math. Soc.
357 (2005), 16631674.
Electronic versions of the paper (from the AMS web site)

Cycling via common divisors; Solution of Problem 11019(b),
with S. Konyagin,
Amer. Math. Monthly
111 (2005), 277278.

On the distribution of imaginary parts of zeros of
the Riemann zeta function , with A. Zaharescu,
J. reine angew. Math.
579 (2005), 145158.

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), 34633468.

Values of the Euler function in various sequences
,
with W. D. Banks, F. Luca, F. Pappalardi and I. E. Shparlinski,
Monatshefte Math.
146 (2005), 119.

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), 495517.

The distribution of integers with at least two divisors in a
short interval , with G. Tenenbaum,
Quart. J. Math. Oxford
58 (2007), 187201.

Generalized Smirnov statistics and the distribution of prime
factors ,
Funct. Approx. Comm. Math.
37.1 (2007), 119129.

Localized large sums of random variables ,
with G. Tenenbaum,
Stat. Prob. Letters 78 (2008), 8489.

Sharp Probability estimates for generalized Smirnov
statistics ,
Monatshefte Math. 153 (2008), 205216.

The distribution of integers with a divisor in a given
interval ,
Annals of Math.
(2) 168 (2008), 367433.

Integers with a divisor in (y,2y] ,
Anatomy of Integers (JeanMarie De Koninck, Andrew Granville, and Florian
Luca, eds), CRM Proc. and Lect. Notes 46 , Amer. Math. Soc.,
Providence, RI, 2008, 6580.
Updated, simplified version (2012)

Generalized Euler constants ,
with H. G. Diamond,
Math. Proc. Cambridge Phil. Soc. 145 (2008), 2741.

Divisors of the Euler and Carmichael functions,
with Y. Hu,
Acta Arithmetica 133 (2008), 199208.

On curves over finite fields with Jacobians of small
exponent, with I. E. Shparlinski,
Int. J. Number Theory 4 (2008), 819826.

On the distribution of imaginary parts of zeros
of the Riemann zeta function, II , with K. Soundararajan
and A. Zaharescu,
Math. Annalen
343 (2009), 487505.

Diophantine approximation with arithmetic functions ,
with E. Alkan and A. Zaharescu,
Trans. Amer. Math. Soc. 361 (2009), 22632275.

On the largest prime factor of the Mersenne numbers ,
with F. Luca and I. E. Shparlinski,
Bull. Austr. Math. Soc. 79 (2009), 455463.

Sharp probability estimates for random walks with barriers
,
Prob. Th. Rel. Fields 145 (2009), 269283.

Diophantine approximation with arithmetic functions, II ,
with E. Alkan and A. Zaharescu, Bull. London Math. Soc.
41 (2009), 676682.

Common values of the arithmetic functions
φ and σ , with Florian Luca and Carl Pomerance,
Bull. London Math. Soc. 42 (2010), 478488.

Geometric Properties of Points on Modular Hyperbolas ,
with Mizan Khan and Igor Shparlinski,
Proc. Amer. Math. Soc. 138 (2010), 41774185.

On the divisibility of Fermat quotients ,
with J. Bourgain, S. V. Konyagin and I. E. Shparlinski,
Michigan Math. J.
59 (2010), 313328.

Prime chains and Pratt trees ,
with Sergei V. Konyagin and Florian Luca,
Geom. Funct. Anal. 20 (2010), 12311258.

Chebyshev's bias for products of two primes , with Jason Sneed,
Experim. Math. 19 (2010), 385398.

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.

Explicit constructions of RIP matrices and related
problems , with J. Bourgain, S. J. Dilworth, S. Konyagin
and D. Kutzarova,
Duke Math. J. 159 (2011), 145185.

Breaking the k^{2} 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), 637644.

On common values of φ(n) and σ(m), I . with
Paul Pollack, Acta Math. Hungarica 133 (2011), 251271.

A problem of Ramanujan, Erdos and Katai on the iterated divisor
function
,
with Y. Buttkewicz, C. Elsholtz and J.C. SchlagePuchta,
International Mathematical Research
Notices 2012 , 40514061.

On common values of φ(n) and σ(m), II . with
Paul Pollack,
Algebra and Number Theory 6 (2012), no. 8, 16691696.
 On groups with perfect order
subsets , with Sergei Konyagin and Florian Luca. Moscow
J. Comb. Number Th. 2 (2012), 297312.

PoissonDirichlet branching random walks .
with Louigi AddarioBerry,
Ann. Appl. Prob. 23 , (1) (2013), 283307.
 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), 127137.
 On nonintersecting arithmetic
progressions , with Régis de la Bretèche and Joseph Vandehey,
Acta Arithmetica 157 (2013), 381392.
 The prime number
race and zeros of Lfunctions off the critical line. III.
with Sergei Konyagin and Youness Lamzouri,
Quart. J. Math. Oxford
64 (2013), 10911098.

Values of the Euler φfunction not divisible by
a given odd prime, and the distribution of EulerKronecker constants for
cyclotomic fields , with Florian Luca and Pieter Moree,
Math. Comp. 83 (2014), no. 287, 14471476.
 Sieving very thin sets of primes,
and Pratt trees with missing primes .
International Mathematical Research
Notices 2014 (2014), 29552971.
 On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing ,
with Trevor D. Wooley, Acta Mathematica 213 (2014), 199236.
 The image of
Carmichael's λfunction , with Florian Luca and Carl
Pomerance,
Algebra and Number Theory 8 (2014), 20092025.
 Unnormalized differences between zeros of Lfunctions , with Alexandru Zaharescu,
Compositio Math.
151 (2015), 230252.
 Large gaps between
consecutive prime numbers containing perfect powers , with
D. R. HeathBrown and Sergei Konyagin, in the book
Analytic Number Theory , in honor of Helmut Maier's 60th
birthday, C. Pomerance and M.Th. Rassias (eds.), SpringerVerlag, 2015,
pp. 8392.
 On the parity of the number
of small divisors of n ,
with F. Luca, C. Pomerance and J. Shallit,
in the book
Analytic Number Theory , in honor of Helmut Maier's 60th
birthday, C. Pomerance and M.Th. Rassias (eds.), SpringerVerlag, 2015,
pp. 93100.
Expository/Survey/Announcement Papers
 The distribution of totients,
ERA Amer. Math. Soc. ,
4 (1998), 2734.
PS, DVI or TeX source.

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), 6791.

Recent progress on the estimation of Weyl sums
, Modern Problems of Number Theory and its
Applications; Topical Problems Part II (Tula, Russia, 2001).
(2002), 4866.
 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, 111120. 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).
 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,
97108.
Updated version (with sketch of a different proof of the main result).
PDF file (13 pages).
Preprints (submitted, not yet in print)
 Large gaps between
consecutive prime numbers , with Ben Green, Sergei Konyagin
and Terence Tao, Annals of
Math. , to appear. 3October2015 revision.
 Long gaps between
consecutive prime numbers , with Ben Green, Sergei Konyagin,
James Maynard and and Terence Tao, 39 pages. 22FEB2015 revision
 Chains of large gaps between primes , with James Maynard and Terence Tao, 16 pages.
 Permutations
fixing a kset , with Sean Eberhard and Ben Green,
IMRN , to appear,
16 pages.
 Invariable generation of
the symmetric group
, with Sean Eberhard and Ben Green, 13 pages.
 Simultaneous distributions of
fractional parts of Riemann zeta zeros , with Xianchang Meng
and Alexandru Zaharescu, 15 pages.
 On the smallest simultaneous power nonresidue modulo a prime , with Moubariz Z. Garaev and Sergei V. Konyagin, 15 pages.