Some of My Preprints (Not Necessarily the Published Version)

Newton polygons and the Prouhet-Tarry-Escott problem , with Maria Markovich, submitted. [pdf]

Further irreducibility criteria for polynomials with non-negative coefficients , with Morgan Cole and Scott Dunn, Acta Arith., to appear. [pdf]

On the irreducibility of a polynomial associated with the Strong Factorial Conjecture , with Brady Rock, Colloquium Mathematicum, to appear. [pdf]

Starting with gaps between k-free numbers , with Sid Graham and Ognian Trifonov, International Journal of Number Theory 11 (2015), 1411-1435. [pdf]

Colorings of Pythagorean triples within colorings of the positive integers , with Joshua Cooper, Joshua Harrington and Daniel White, Journal of Combinatorics and Number Theory 6 (2014), 1-16. [pdf]

Is every polynomial with integer coefficients near an irreducible polynomial? , Elemente der Mathematik 69 (2014), 130-143. [pdf]

49598666989151226098104244512918 , with Sam Gross, Journal of Number Theory 137 (2014), 16-49. [pdf]

The non-cyclotomic part of f(x) x^n + g(x) and roots of reciprocal polynomials off the unit circle , with Edward Dobrowolski and Andrew Vincent, International Journal of Number Theory 9 (2013), 1865-1877. [pdf]

On classifying Laguerre polynomials which have Galois group the alternating group , with Pradipto Banerjee, Carrie E. Finch and J Russell Leidy, Journal de Theorie des Nombres de Bordeaux 25 (2013), 1-30. [pdf]

A polynomial investigation inspired by work of Schinzel and Sierpinski , with Joshua Harrington, Acta Arith. 155 (2012), 149-161. [pdf]

Solving n(n+d)...(n+(k-1)d) = b y^2 with P(b) <= Ck , with Shanta Laishram and N. Saradha, International Journal of Number Theory 8 (2012), 161-173.. [pdf]

The distance to an irreducible polynomial, II , with Michael Mossinghoff, Math. Comp. 81 (2012), 1571-1585. [pdf]

Laguerre polynomials with Galois group A_m for each m , with Travis Kidd and Ognian Trifonov, Journal of Number Theory 132 (2012), 776-805. [pdf]

Composites that remain composite after changing a digit , Mark Kozek, Charles Nicol and John Selfridge, Journal of Combinatorics and Number Theory 2 (2011), 25-36. [pdf]

On a polynomial conjecture of Pal Turan , with Pradipto Banerjee, Acta Arithmetica 143 (2010), 239--255. [pdf]

On values of d(n!)/m!, phi(n!)/m! and sigma(n!)/m! , with Dan Baczkowski, Florian Luca and Ognian Trifonov, International Journal of Number Theory 6 (2010), 1199-1214. [pdf]

On the factorization of consecutive integers , with Michael Bennett and Ognian Trifonov, Journal fur die reine und angewandte Mathematik (Crelle) 629 (2009), 171-200. [pdf]

Yet another generalization of the Ramanujan-Nagell equation , with Michael Bennett and Ognian Trifonov, Acta Arithmetica 134 (2008), 211-217. [pdf]

On powers associated with Sierpinski numbers, Riesel numbers and Polignac's conjecture , with Carrie Finch and Mark Kozek, Journal of Number Theory 128 (2008), 1916-1940. [pdf] [data]

Irreducibility and greatest common divisor algorithms for sparse polynomials , with Andrew Granville and Andrzej Schinzel, Number Theory and Polynomials (ed. James McKee and Chris Smyth), LMS Lecture Note Series 352, Cambridge Univ. Press, 2008, pp. 155-176. [pdf]

T. N. Shorey's influence in the theory of irreducible polynomials , with Carrie Finch and J Russell Leidy, Diophantine Equations (ed. N. Saradha), Narosa Publ. House, New Delhi, 2008, pp. 77-102. [pdf]

Galois groups of polynomials arising from circulant matrices , with Florian Luca, Pante Stanica and Robert Underwood, Journal of Number Theory 128 (2008), 59-70. [pdf]

Sieving by large integers and covering systems of congruences , with Kevin Ford, Sergei Konyagin, Carl Pomerance and Gang Yu, Journal of the American Mathematical Society 20 (2007), 495-517. [pdf]

On the irreducibility of a truncated binomial expansion , with Angel Kumchev and Dmitrii Pasechnik, Rocky Mountain Journal of Math. 37 (2007), 455-464. [pdf]

Two Diophantine approaches to the irreducibility of certain trinomials , with Florian Luca, Pante Stanica and Robert Underwood, Acta Arithmetica 128 (2007), 149-156. [pdf]

On three questions concerning 0,1-polynomials , with Carrie Finch and Charles Nicol, Journal de Theorie des Nombres de Bordeaux 118 (2006), 357-370. [pdf]

Irreducibility testing of lacunary 0,1-polynomials , with Douglas Meade, Journal of Algorithms 55 (2005), 21-28. [pdf]

A generalization of a third irreducibility theorem of I. Schur , with Martha Allen, Acta Arith. 114 (2004), 183-197. [pdf]

On the irreducibility of 0,1-polynomials of the form f(x) x^n + g(x) , with Manton Matthews, Jr., Colloq. Math. 99 (2004), 1-5. [pdf]

On testing the divisibility of lacunary polynomials by cyclotomic polynomials , with Andrzej Schinzel, Math. Comp. 73 (2004), 957-965. [pdf]

A generalization of a second irreducibility theorem of I.Schur , with Martha Allen, Acta Arith. 109 (2003), 65-79. [pdf]

On the irreducibility of a certain class of Laguerre polynomials , with Richard Williams, J. Number Theory 100 (2003), 229-250. [pdf]

On coverings of the integers associated with an irreducibility theorem of A. Schinzel. Number theory for the millennium, II (Urbana, IL, 2000), A K Peters, Natick, MA, 2002, 1-24. [pdf]

On the irreducibility of the generalized Laguerre polynomials, with Tsit-Yuen Lam, Acta Arith. 105 (2002), 177-182. [pdf]

The irreducibility of the Bessel polynomials, with Ognian Trifonov, J. Reine Angew. Math. 550 (2002), 125-140. [pdf]

A distribution problem for powerfree values of irreducible polynomials, with Brian Beasley, Periodica Math. Hungarica 42 (2001), 123-144. [pdf]

On an irreducibility theorem of A. Schinzel associated with coverings of the integers, with Kevin Ford and Sergei Konyagin, Illinois J. Math. 44 (2000), 633-643. [pdf]

Classes of polynomials having only one non-cyclotomic irreducible factor, with Alexander Borisov, Tsit-Yuen Lam, and Ognian Trifonov, Acta Arith., 90 (1999), 121-153. [pdf]

On the factorization of polynomials with small Euclidean norm , Number theory in progress, Vol.~1 (Zakopane-Ko\'scielisko, 1997), de Gruyter, Berlin, 1999, 143-163. [pdf]

An extension of a theorem of Ljunggren , with Ikhalfani Solan, Math. Scand., 84 (1999), 5-10. [pdf]

On a limit point associated with the abc-conjecture, with Sergei Konyagin, Colloquium Mathematicum, 76 (1998), 265-268. [pdf]

Norms of factors of polynomials , with Ikhalfani Solan, Acta Arith., 82 (1997), 243-255. [pdf]

Squarefree values of polynomials and the abc-conjecture, with Jerzy Browkin, George Greaves, and Andrzej Schinzel, Sieve Methods, Exponential Sums, and their Applications in Number Theory, edited by G. Greaves, G. Harman, and M. Huxley, Cambridge Univ. Press, 1997, pp. 65-85. [pdf]

The distribution of fractional parts with applications to gap results in number theory, with Ognian Trifonov, Proc. London Math. Soc. (3) 73 (1996), 241-278. [pdf]

A generalization of an irreducibility theorem of I. Schur, Analytic Number Theory: Proceedings of a Conference in Honor of Heini Halberstam, Volume 1, edited by B.C. Berndt, H.G. Diamond, and A.J. Hildebrand, Birkhauser, Boston, 1996, 371-396. [pdf]

Squarefree values of polynomials all of whose coefficients are 0 and 1, with Sergei Konyagin, Acta Arith., 74 (1996), 191-205. [pdf]

The irreducibility of all but finitely many Bessel polynomials, Acta Math., 174 (1995), 383-397. [pdf]

The distribution of squarefull numbers in short intervals, with Ognian Trifonov, Acta Arith., 67 (1994), 323-333. [pdf]

Powerfree values of binary forms, Journal of Number Theory, 49 (1994), 250-268. [pdf]

The minimal Euclidean norm of an algebraic number is effectively computable, with Michael Robinson and Ferrell Wheeler, Journal of Algorithms, 16 (1994), 309-333. [pdf]

On the distribution of gaps between squarefree numbers, Mathematika, 40 (1993), 88-101. [pdf]

A result on the digits of a^n, with Richard Blecksmith and Charles Nicol, Acta Arith., 64 (1993), 331--339. [pdf]

Short interval results for k-free values of irreducible polynomials, Acta Arith., 64 (1993), 249--270. [pdf]

An estimate for the number of reducible Bessel Polynomials of bounded degree, with Sid Graham, Colloquium Mathematicum, 65 (1993), 65-68. [pdf]

Squarefree values of polynomials, Acta Arith., 60 (1992), 213-231. [pdf]

On gaps between squarefree numbers II, with Ognian Trifonov, Journal of the London Math. Soc. (2), 45 (1992), 215-221. [pdf]