Papers

Note: Clicking on "pdf" or "postscript" will bring up a pdf or postscript verion of the paper.

L. DeMarco, D. Ghioca, H. Krieger, K. Nguyen, T. J. Tucker, H. Ye; "Bounded height in families of dynamical systems." To appear in Int. Math. Res. Not. IMRN. (preprint pdf)

L.-C. Hsia and T. J. Tucker. "Greatest common divisors of iterates of polynomials." To appear in Algebra Number Theory (preprint pdf)

A. Bridy and T. Tucker. "ABC implies a Zsigmondy principle for ramification." To appear in J. Number Theory. (preprint pdf)

D. Ghioca, L.-C. Hsia, and T. J. Tucker "On a variant of the Ailon-Rudnick theorem in finite characteristic". New York J. Math. 23 (2017), 213--225. (preprint pdf)

D. Ghioca, L. C. Hsia, and T. J. Tucker. "Unlikely intersection for two-parameter families of polynomials." Int. Math. Res. Not. IMRN 2016, no. 24, 7589--7618. (preprint pdf)

J. Juul, P. Kurlberg, K. Madhu, and T. J. Tucker. "Wreath products and proportions of periodic points." Int. Math. Res. Not. IMRN 2016, no. 13, 3944-3969. (preprint pdf)

J. P. Bell, D. Ghioca, and T. J. Tucker "The dynamical Mordell-Lang conjecture." Mathematical Surveys and Monographs, 210. American Mathematical Society, Providence, RI, 2016.

J. P. Bell, D. Ghioca, and T. J. Tucker. "The Dynamical Mordell-Lang problem for Noetherian spaces." Funct. Approx. Comment. Math. 53 (2015), no. 2, 313--328. (preprint pdf)

D. Ghioca, K. Nguyen, and T. J. Tucker. "Portraits of preperiodic points for rational maps." Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 1, 165--186. (preprint pdf).

H. Krieger, A. Levin, Z. Scherr, T. J. Tucker, Y. Yasufuku, M. Zieve. "Uniform Boundedness of S-Units in Arithmetic Dynamics." Pacific J. Math. 274 (2015), no. 1, 97--106. (preprint pdf).

P. Corvaja, V. Sookdeo, T. J. Tucker, and U. Zannier. "Integral points in two-parameter orbits." Crelle 706 (2015), 19--33. (preprint pdf)

D. Ghioca, L.-C. Hsia, and T. J. Tucker. "Preperiodic points for families of rational maps." Proc. London Math. Soc. (3) 110 (2015), no. 2, 395--427. (preprint pdf)

J. P. Bell, D. Ghioca, and T. J. Tucker. "Applications of p-Adic Analysis for Bounding Periods of Subvarieties Under Etale Maps." Int. Math. Res. Not. IMRN 2015, no. 11, 3576--3597. (preprint pdf)

T. J. Tucker. ``Integer points in arithmetic sequences.'' Bull. Inst. Math. Acad. Sin. (N.S.) 9 (2014), no. 4, 633--639. (preprint pdf)

D. Ghioca, L.-C. Hsia, and T. J. Tucker. ``Preperiodic points for families of polynomials''. Algebra Number Theory 7 (2013). (preprint pdf)

R. Benedetto, D. Ghioca, B. Hutz, P. Kurlberg, T. Scanlon, and T. J. Tucker. ``Periods of rational maps modulo primes''. Math. Ann. 355 (2013), 637--660. (preprint pdf)

C. Gratton, K. Nguyen, and T. J. Tucker. ``ABC implies primitive prime divisors in arithmetic dynamics.'' Bulletin of the LMS (2013); doi: 10.1112/blms/bdt049. (preprint pdf)

D. Ghioca, T. J. Tucker, and S.-W. Zhang. "Towards a dynamical Manin-Mumford conjecture." Int. Math. Res. Not. Vol. 2011, DOI: 10.1093/imrn/rnq283, 14 pages. (preprint pdf)

D. Ghioca, T. J. Tucker, and M. E. Zieve. "The Mordell-Lang question for endomorphisms of semiabelian varieties." Journal de Théor. Nombres Bordeaux 23 (2011), 645--666. (preprint pdf)

C. Petsche, L. Szpiro, and T. J. Tucker. "Dynamical Pairing Between Two Rational Maps." Trans. Amer. Math. Soc. 364 (2012), 1687--1710 (preprint pdf)

R. Benedetto, D. Ghioca, P. Kurlberg, T. J. Tucker. "A gap principle for dynamics." Compositio Math. 146 (2010), 1056--1072 . (preprint pdf)

J. P. Bell, D. Ghioca, and T. J. Tucker. "The dynamical Mordell-Lang problem for etale maps." Amer. J. Math. 132 (2010), 1655--1675 (preprint pdf)

D. Ghioca, T. J. Tucker, and M. E. Zieve. "Linear relations between polynomial orbits." Duke Math. J. 161 (2012), 1379--1410. (preprint pdf)

D. Ghioca and T. J. Tucker. "Proof of a dynamical Bogomolov conjecture for lines under polynomial actions." Proc. Amer. Math Soc. 138 (2010), 937-942. (preprint pdf)

D. Ghioca and T. J. Tucker. "Periodic points, linearizing maps, and the dynamical Mordell-Lang problem." J. Number Theory 129 (2009), 1392--1403. (preprint pdf)

X. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes, T. J. Tucker, M. E. Zieve. "Uniform bounds on pre-images under quadratic dynamical systems." Math. Res. Lett. 16 (2009), 87--101. (preprint pdf)

S.-I. Ih and T. J. Tucker. "A finiteness property for preperiodic points of Chebyshev polynomials." Int. J. Number Theory 6 (2010), 1011--1025. (preprint pdf)

R. Benedetto, D. Ghioca, P. Kurlberg, T. J. Tucker, U. Zannier. "The dynamical Mordell-Lang conjecture." Math Ann. 352 (2012), 1--26 (preprint pdf)

D. Ghioca, T. J. Tucker, and M. E. Zieve. "Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture." Inventiones Math. 171 (2008), 463--483. (preprint pdf)

D. Ghioca and T. J. Tucker. "p-adic logarithms for polynomial dynamics." 11 pages, the results of this preprint have been subsumed by recent more general results. (preprint pdf)

D. Ghioca and T. J. Tucker. "Mordell-Lang and Skolem-Mahler-Lech theorems for endomorphisms of semiabelian varieties." 13 pages, the results of this preprint have been subsumed by recent more general results. (preprint pdf)

D. Ghioca and T. J. Tucker. "A dynamical version of the Mordell-Lang conjecture for the additive group." Compositio Math., 144 (2008), 304--316. (preprint pdf)

D. Ghioca and T. J. Tucker. "Siegel's theorem for Drinfeld modules." Math. Ann. 339 (2007), 37--60. (preprint pdf)

D. Ghioca and T. J. Tucker. "Equidistribution and integral points for Drinfeld modules." Trans. Amer. Math. Soc. 360 (2008), 4863--4887. (preprint pdf)

L. Szpiro and T. J. Tucker. "Equidistribution and generalized Mahler measures." In, Goldfeld, D.; Jorgenson, J.; Jones, P.; Ramakrishnan, D.; Ribet, K.A.; Tate, J., editors, Number Theory, Analysis and Geometry: In Memory of Serge Lang, pages 609--638, Springer-Verlag, New York, 2012. (preprint pdf)

L. Szpiro and T. J. Tucker. "A Shafarevich-Faltings theorem for rational maps." Pure Appl. Math. Q. 4 (2008), 715--728. (preprint pdf)

L. Szpiro and T. J. Tucker. "One half log discriminant." Diophantine Geometry Proceedings (Pisa, April-July 2005), Publications of the Scuola Normale Superiore, Pisa, 2007. (preprint Postscript)

R. M. Guralnick, T. J. Tucker, and M. E. Zieve. "Exceptional covers and bijections on rational points." Int. Math. Res. Not., Vol. 2007, article ID rnm004, 19 pages. (preprint pdf)

J. Pineiro, L. Szpiro, and T. J. Tucker. "Mahler measure for dynamical systems on P¹ and intersection theory on a singular arithmetic surface." In, F. Bogomolov and Y. Tschinkel, editors, Geometric methods in algebra and number theory, Progress in Math 235, pages 219--250, Birkhauuser, 2004. (preprint pdf)

P. Cutter, A. Granville, and T. J. Tucker. "The number of fields generated by the square root of a given polynomial." Canad. Math. Bull. 46 (2003), 71--79. (preprint pdf)

A. Granville and T. J. Tucker. "It's as easy as abc." Notices Amer. Math. Soc. 49 (2002), no. 10, 1224--1231.(preprint pdf)

D. Lorenzini and T. J. Tucker. "Thue equations and the method of Chabauty-Coleman." Inventiones Math. 148 (2002), 47--77. (preprint pdf)

T. J. Tucker. "Irreducibility, Brill-Noether loci, and Vojta's inequality." Trans. Amer. Math. Soc. 354 (2002), 3011 -- 3029. (preprint pdf)

X. Song and T. J. Tucker. "Arithmetic discriminants and morphisms of curves." Trans. Amer. Math. Soc. 353 (2001) 1921--1936. (preprint pdf)

X. Song and T. J. Tucker. "Dirichlet's Theorem, Vojta's inequality, and Vojta's conjecture." Compositio Math. 116 (1999), 219--238. (preprint pdf)
Last modified: Thu Aug 31 15:31:00 EDT 2017