This list is arranged in reverse chronological order - anytime a preprint is added or the status of a manuscript is updated, it is moved to the top of the list.
abc triples, with Winnie Miao, in preparation.
Averages of the number of points on elliptic curves, with Paul Pollack and Ethan Smith, Algebra Number Theory 8 (2014), no. 4, 813-839.
Appendix to 'The frequency of elliptic curve groups over prime finite fields', with Chantal David and Ethan Smith, submitted.
Squarefree values of trinomial discriminants, with David W. Boyd and Mark Thom, submitted.
Lower bounds for sumsets of multisets in Zp2, with Alexis Peilloux and Erick B. Wong, Integers 13 (2013), #A72 (17pp).
Optimal primitive sets with restricted primes, with William D. Banks, Integers 13 (2013), #A69 (10pp).
Nonzero values of Dirichlet L-functions in vertical arithmetic progressions, with Nathan Ng, Int. J. Number Theory 9 (2013), no. 4, 813-843.
The average least character nonresidue and further variations on a theme of Erdős, with Paul Pollack, J. London Math. Soc. 87 (2013), no. 1, 22-42.
Inequities in the Shanks–Rényi prime number race: an asymptotic formula for the densities, with Daniel Fiorilli, J. Reine Angew. Math. 676 (2013), 121-212.
An Erdős–Kac theorem for products of additive functions, in preparation.
The number of subgroups in the multiplicative group modulo n, in preparation.
Inclusive prime number races, with Nathan Ng, in preparation.
Polynomials whose coefficients are related to the Goldbach conjecture, with Peter Borwein, Kwok-Kwong Stephen Choi, and Charles L. Samuels, JP J. Algebra Number Theory Appl. 26 (2012), no. 1, 33-63.
Primitive points in lattice polygons, with Imre Barany, Eric Naslund, and Sinai Robins, in preparation.
Comparative prime number theory: a survey, with Justin Scarfy, unpublished (37 pages).
Primitive sets with large counting functions, with Carl Pomerance, Publ. Math. Debrecen 79 (2011), no. 3-4, 521-530.
Erdős–Turán with a moving target, equidistribution of roots of reducible quadratics, and Diophantine quadruples, with Scott Sitar, Mathematika 57 (2011), 1-29.
Roots of unity and nullity modulo n, with Steven Finch and Pascal Sebah, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2729-2743.
Structural insights and elegant applications: a book review of The Anatomy of Integers, CMS Notes 41 (2009), no. 5, 4-5.
Nonzero values of Dirichlet L-functions at linear combinations of other zeros, with Nathan Ng, in preparation.
An Erdős–Kac theorem for the number of prime factors of multiplicative orders, with Leo Goldmakher, in preparation.
The supremum of autoconvolutions, with applications to additive number theory, with Kevin O'Bryant, Illinois J. Math. 53 (2010), no. 1, 219-236.
A product of Gamma function values at fractions with the same denominator, unpublished (3 pages).
Almost all integer matrices have no integer eigenvalues, with Erick B. Wong, Amer. Math. Monthly 116 (2009), no. 7, 588-597.
A simple polynomial for a transposition, Mathematical Advance in Translation 27 (2008), no. 4, 382-384.
The number of 2×2 integer matrices having a prescribed integer eigenvalue, with Erick B. Wong, Algebra & Number Theory 2 (2008), no. 8, 979-1000.
Sets that contain their circle centers, College Math. J. 39 (2008), no. 5, 357-366.
Many sets have more sums than differences, with Kevin O'Bryant, Additive Combinatorics (proceedings of the CRM–Clay School on Additive Combinatorics, Centre de Recherches Mathématiques, April 2006), ed. Andrew Granville, Melvyn B. Nathanson, and József Solymosi, CRM Proceedings & Lecture Notes, 43, American Mathematical Society (Providence, RI, 2007), 287-305.
A simple polynomial for a simple transposition, Amer. Math. Monthly 115 (2008), no. 1, 57-60.
The symmetric subset problem in continuous Ramsey theory, with Kevin O'Bryant, Experiment. Math. 16 (2007), no. 2, 145-165.
Constructions of generalized Sidon sets, with Kevin O'Bryant, J. Combin. Theory Ser. A 113 (2006), no. 4, 591-607.
Prime number races, with Andrew Granville, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
The iterated Carmichael λ-function and the number of cycles of the power generator, with Carl Pomerance, Acta Arith. 118 (2005), no. 4, 305-335.
Dimensions of the spaces of cusp forms and newforms on Γ0(N) and Γ1(N), J. Number Theory 112 (2005), no. 2, 298-331.
Carreras de números primos, with Andrew Granville, Gac. R. Soc. Mat. Esp. 8.1 (2005), 197-240.
The unreasonable effectualness of continued function expansions, J. Aust. Math. Soc. 77 (2004), 305-319.
Inequities in three-way prime number races, in preparation.
The limiting curve of Jarník's polygons, Trans. Amer. Math. Soc. 355 (2003), no. 12, 4865-4880.
An asymptotic formula for the number of smooth values of a polynomial, J. Number Theory 93 (2002), no. 2, 108-182.
Compactness theorems for geometric packings, J. Combin. Theory Ser. A 97 (2002), 225-238.
Absolutely abnormal numbers, Amer. Math. Monthly 108 (2001), no. 8, 746-754.
Restoring fairness to Dukego, More Games of No Chance (proceedings of the Combinatorial Game Theory Research Workshop, MSRI, July 2000), ed. R. J. Nowakowski, Cambridge University Press (Cambridge, 2002), 79-87.
Polynomial values free of large prime factors, with Cécile Dartyge and Gérald Tenenbaum, Periodica Math. Hungarica 43 (2001), no. 1-2, 111-119.
Biases in the Shanks–Rényi prime number race, with Andrey Feuerverger, Experiment. Math. 9 (2000), no. 4, 535-570.
Denser Egyptian fractions, Acta Arith. 95 (2000), no. 3, 231-260.
Asymmetries in the Shanks–Rényi prime number race, Number Theory for the Millennium (proceedings of the Millennial Conference on Number Theory, University of Illinois, Urbana–Champaign, May 2000), ed. M. A. Bennett et. al., A K Peters (Natick, MA, 2002), vol. II, 403-415.
Farmer Ted goes natural, Math. Mag. 72 (1999), no. 4, 259-276.
Dense Egyptian fractions, Trans. Amer. Math. Soc. 351 (1999), no. 9, 3641-3657.
The smallest solution of φ(30n+1)<φ(30n) is ..., Amer. Math. Monthly 106 (1999), no. 5, 449-451.
Uniform bounds for the least almost-prime primitive root, Mathematika 45 (1998), no. 1, 191-207.
The least prime primitive root and the shifted sieve, Acta Arith. 80 (1997), no. 3, 277-288.
Solubility of systems of quadratic forms, Bull. London Math. Soc. 29 (1997), no. 4, 385-388.
The above papers are the intellectual property of Greg Martin, with copyrights held by the journals in which they appear. All rights reserved.