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