Some of the following articles may be downloaded in
Adobe Acrobat (PDF) format.
In order to read these files, you may
have to download the Adobe Acrobat Reader.
Click on the icon at the right to download this free software from
Adobe.
T. T. H. An, W. Cherry,
and N. V. Phuong, A Non-Archimedean Second Main Theorem for Hypersurfaces
in Subgeneral Position. Preprint available on the arXiv:
2408.07210
W. Cherry and
Z. Ye,
Nevanlinna's
Theory of Value Distribution. The Second Main Theorem
and its Error Terms,
Springer Monographs in Mathematics,
Springer-Verlag,
2001.
MR 2002h:30030
Click the following to order from:
Springer
Amazon.com.
Click here for a list of
errata and a discussion of number theoretic error terms.
S. Lang
and W. Cherry, Topics in Nevanlinna
Theory, Lecture Notes in Mathematics 1433, Springer-Verlag,
1990. MR 91k:32025
M. Fincher, H. Olney, and W. Cherry, Some projective distance inequalities for simplices in complex projective space, Inv@lve, a journal of mathematics 8 (2015), 707-719; preliminary version available on the arXiv: math: 1407.5850
W. Cherry, Existence of GCD's and Factorization in Rings of Non-Archimedean Entire Functions in J. Araujo, B. Diarra, and A. Escassut, eds., Advances in Non-Archimedean Analysis, Contemporary Mathematics 551 (2011), 57-70. MR2882389 Preprint available on the arXiv: 1007.0984
W. Cherry and C. Toropu, Generalized ABC theorems for non-Archimedean entire functions of several variables in arbitrary characteristic, Acta Arithmetica 136 (2009), 351-384. Preliminary version available on the preprint arXiv: MR2476602 arXiv:0807.4332.
Ta Thi Hoai An, W. Cherry and
Julie Tzu-Yueh
Wang, Algebraic Degeneracy
of Non-Archimedean Analytic Maps,
Indag. Math.
19 (2008), 481-492.
MR 2010b:32031
Preliminary version available on the preprint arXiv:
arXiv:0708.0401.
Click here for the Erratum.
W. Cherry and A. Eremenko, Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements, Pure Appl. Math. Q. 7 (2011), 199-221. MR2900169 Preliminary version available on the preprint arXiv: math.CV 0607743.
W. Cherry and Min Ru, Rigid Analytic Picard Theorems, Amer. J. Math. 126 (2004), 873-889. MR 2005d:32022
W. Cherry and Julie Tzu-Yueh Wang, Non-Archimedean Analytic Maps to Algebraic Curves, in W. Cherry and C.-C. Yang, Value Distribution Theory and Complex Dynamics, Contemporary Mathematics 303, American Mathematical Society, 2002, pages 7-36. MR 2004b:30080
W. Cherry and Julie Tzu-Yueh Wang, Uniqueness polynomials for entire functions, Internat. J. Math. 13 (2002), 323-332. MR 2003d:30033
A. Boutabaa,
W. Cherry, and
A. Escassut,
Unique range sets in positive characteristic,
Acta
Arith. 103 (2002), 169-189.
MR 2003m:30067
Click here
for the Erratum.
W. Cherry, Applications of explicit error terms in Nevanlinna theory, in R. P. Gilbert et al. (eds.), Recent Developments in Complex Analysis and Computer Algebra, Kluwer Academic Publishers, 1999, 47-67. MR 2001e:30047
M. Bonk and W. Cherry, Metric distortion and triangle maps, Annales Academiæ Scientiarium Fennicæ Mathematica 24 (1999), 489-510. MR 2001b:30009
W. Cherry and C.-C. Yang, Uniqueness of non-Archimedean entire functions sharing sets of values counting multiplicity, Proc. Amer. Math. Soc. 127 (1999), 967-971. MR 99f:11154
W. Cherry, A survey of Nevanlinna theory over non-Archimedean fields, Bull. Hong Kong Math. Soc. 1 (1997), 235-249. MR 99a:32047
W. Cherry and Z. Ye, Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem , Trans. Amer. Math. Soc. 349 (1997), 5043-5071. MR 98c:11072
M. Bonk and W. Cherry, Bounds on spherical derivatives for maps into regions with symmetries, J. Anal. Math. 69 (1996), 249-274. MR 97k:30059
W. Cherry, A non-Archimedean analog of the Kobayashi semi-distance and its non-degeneracy on Abelian varieties, Illinois J. Math. 40 (1996), 123-140. MR 97b:32049
W. Cherry, Non-archimedean analytic curves in Abelian varieties, Math. Ann. 300 (1994), 393-404. MR 96i:14021
W. Cherry, "The Nevanlinna error term
for coverings, generically surjective case," in W. Stoll, ed., Proceedings
of the Symposium on Value Distribution Theory in Several Complex Variables,
Notre Dame Mathematical Lectures 12,
University of Notre Dame
Press, 1992. MR 95b:30040
Guest Editor (with Ta Thi Hoai An), Vietnam Journal of Mathematics, volume 39, number 3 (2011).
W. Cherry and
C.-C. Yang,
Value Distribution Theory and Complex Dynamics, Contemporary Mathematics
303, American Mathematical Society, 2002.
MR 2003g:30001
W. Cherry, Yi's Unique Range Set Construction in the Number Field Case. Also available on the preprint arXiv: arXiv:math/0605492.
W. Cherry,
Non-Archimedean big Picard theorems.
Also available on the preprint arXiv:
arXiv:math/0207081.
W. Cherry, The potential theoretic method of Eremenko and Sodin, three lectures in the Summer School on Topics On Nevanlinna Theory and Complex Hyperbolicities at the Shanghai Center for Mathematical Sciences, July 2019: Lecture #1, Lecture #2 Appendix to Lecture #2 Lecture #3
W. Cherry, Non-Archimedean Analytic Curves in Algebraic Varieties, video of my lecture at the 2015 BIRS workshop on Distribution of Rational and Holomorphic Curves.
W. Cherry, Value Distribution Theory of non-Archimedean Meromorphic Functions, video of my lecture at the 2014 BIRS workshop on Vojta Conjectures.
W. Cherry, Analogies Between Numbers and Functions, a lecture to undergraduates at a summer program at the Institute of Mathematics, Hanoi, Vietnam.
W. Cherry, Non-Archimedean Function Theory, text of a four lecture short course delivered in 2009 at the International Centre for Theoretical Physics in Trieste, Italy. Also available on the preprint arXiv: arXiv:math/0909.4509 and from ICTP.
W. Cherry, Lectures on Holomorphic Curves in Abelian Varieties (rough draft in progress), text of a three lecture series delivered at National Central University in Jhongli, Taiwan in June of 2009.
W. Cherry, Algebraic degeneracy of non-Archimedean analytic maps omitting divisors with sufficiently many components, slides and audio of a lecture given in the Workshop on Complex Hyperbolic Geometry and Related Topics held at the Fields Institute in November 2008.
W. Cherry,
Topics in p-adic function theory,
text of a lecture delivered at the symposium on p-adic Nevanlinna
theory and related topics, held at the
Nippon Institute of Technology,
November 1998.
Return
to William Cherry's home page