This list is arranged by subject - ordered according to the 2010
Mathematics Subject Classification number corresponding to the primary
subject of the paper.
- 11A: Elementary number theory
A simple polynomial for a simple transposition, Amer. Math. Monthly 115 (2008), no. 1, 57-60.
A simple polynomial for a transposition, Mathematical Advance in Translation 27 (2008), no. 4, 382-384.
The smallest solution of φ(30n+1)<φ(30n) is ..., Amer. Math. Monthly 106 (1999), no. 5, 449-451.
- 11B: Sequences and sets
Constructions of generalized Sidon sets, with Kevin O'Bryant, J. Combin. Theory Ser. A 113 (2006), no. 4, 591-607.
Farmer Ted goes natural, Math. Mag. 72 (1999), no. 4, 259-276.
Lower bounds for sumsets of multisets in Zp2, with Alexis Peilloux and Erick B. Wong, Integers 13 (2013), #A72 (17pp).
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.
Optimal primitive sets with restricted primes, with William D. Banks, Integers 13 (2013), #A69 (10pp).
Primitive sets with large counting functions, with Carl Pomerance, Publ. Math. Debrecen 79 (2011), no. 3-4, 521-530.
The supremum of autoconvolutions, with applications to additive number theory, with Kevin O'Bryant, Illinois J. Math. 53 (2010), no. 1, 219-236.
The symmetric subset problem in continuous Ramsey theory, with Kevin O'Bryant, Experiment. Math. 16 (2007), no. 2, 145-165.
- 11D: Diophantine equations
Dense Egyptian fractions, Trans. Amer. Math. Soc. 351 (1999), no. 9, 3641-3657.
Denser Egyptian fractions, Acta Arith. 95 (2000), no. 3, 231-260.
Erdős–Turán with a moving target, equidistribution of roots of reducible quadratics, and Diophantine quadruples, with Scott Sitar, Mathematika 57 (2011), 1-29.
Solubility of systems of quadratic forms, Bull. London Math. Soc. 29 (1997), no. 4, 385-388.
- 11F: Modular forms
Dimensions of the spaces of cusp forms and newforms on Γ0(N) and Γ1(N), J. Number Theory 112 (2005), no. 2, 298-331.
- 11G: Elliptic curves
Averages of the number of points on elliptic curves, with Paul Pollack and Ethan Smith, Algebra Number Theory, to appear (19 pages).
- 11J: Diophantine approximation
The unreasonable effectualness of continued function expansions, J. Aust. Math. Soc. 77 (2004), 305-319.
- 11K: Probabilistic number theory
Absolutely abnormal numbers, Amer. Math. Monthly 108 (2001), no. 8, 746-754.
- 11M: Zeta and L-functions
Nonzero values of Dirichlet L-functions at linear combinations of other zeros, with Nathan Ng, in preparation.
Nonzero values of Dirichlet L-functions in vertical arithmetic progressions, with Nathan Ng, Int. J. Number Theory 9 (2013), no. 4, 813-843.
- 11N: Multiplicative number theory
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.
An asymptotic formula for the number of smooth values of a polynomial, J. Number Theory 93 (2002), no. 2, 108-182.
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.
Biases in the Shanks–Rényi prime number race, with Andrey Feuerverger, Experiment. Math. 9 (2000), no. 4, 535-570.
Carreras de números primos, with Andrew Granville, Gac. R. Soc. Mat. Esp. 8.1 (2005), 197-240.
Comparative prime number theory: a survey, with Justin Scarfy, unpublished (37 pages).
An Erdős–Kac theorem for products of additive functions, in preparation.
An Erdős–Kac theorem for the number of prime factors of multiplicative orders, with Leo Goldmakher, in preparation.
Inclusive prime number races, with Nathan Ng, in preparation.
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.
Inequities in three-way prime number races, in preparation.
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.
The least prime primitive root and the shifted sieve, Acta Arith. 80 (1997), no. 3, 277-288.
The number of subgroups in the multiplicative group modulo n, 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.
Polynomial values free of large prime factors, with Cécile Dartyge and Gérald Tenenbaum, Periodica Math. Hungarica 43 (2001), no. 1-2, 111-119.
Prime number races, with Andrew Granville, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
Roots of unity and nullity modulo n, with Steven Finch and Pascal Sebah, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2729-2743.
Squarefree values of trinomial discriminants, with David Boyd and Mark Thom, submitted.
Structural insights and elegant applications: a book review of The Anatomy of Integers, CMS Notes 41 (2009), no. 5, 4-5.
Uniform bounds for the least almost-prime primitive root, Mathematika 45 (1998), no. 1, 191-207.
- 15: Linear algebra
Almost all integer matrices have no integer eigenvalues, with Erick B. Wong, Amer. Math. Monthly 116 (2009), no. 7, 588-597.
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.
- 33: Special functions
A product of Gamma function values at fractions with the same denominator, unpublished (3 pages).
- 51-52: Geometry
Compactness theorems for geometric packings, J. Combin. Theory Ser. A 97 (2002), 225-238.
The limiting curve of Jarník's polygons, Trans. Amer. Math. Soc. 355 (2003), no. 12, 4865-4880.
Primitive points in lattice polygons, with Imre Barany, Eric Naslund, and Sinai Robins, in preparation.
Sets that contain their circle centers, College Math. J. 39 (2008), no. 5, 357-366.
- 90D: Game theory
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.
The above papers are the intellectual property of Greg Martin, with copyrights held by the journals in which they appear. All rights reserved.