My research interests are in number theory and dynamical systems. For further information please click here to return to my Mathematics Department index page.
Publications:
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Non-Archimedean Koksma inequalities, variation, and Fourier analysis
Clayton Petsche and Naveen Somasunderam
Uniform Distribution Theory, to appear (arxiv)
- Totally T-adic functions of small height
Xander Faber and Clayton Petsche
Rendiconti Lincei Matematica e Applicazioni, Vol. 31 (4), (2020), 699–732 (journal) (arxiv)
- Abelian extensions in dynamical Galois theory
Jesse Andrews and Clayton Petsche
Algebra and Number Theory, Vol. 14 (2020), No. 7, 1981–1999 (journal) (arxiv)
- Attractors associated to a family of hyperbolic p-adic plane automorphisms
Clayton Petsche
Ergodic Theory and Dynamical Systems, Vol. 41 (2020), No. 6, (journal) (arxiv)
- A dynamical construction of small totally p-adic algebraic numbers
Clayton Petsche and Emerald Stacy
Journal of Number Theory, Vol. 202 (2019) 27-36 (journal) (arxiv)
- A Dirichlet approximation theorem for group actions
Clayton Petsche and Jeffrey D. Vaaler
Functiones et Approximatio Commentarii Mathematici, Vol. 60, No. 2 (2019) 263-275 (journal) (arxiv)
- Non-Archimedean Hénon maps, attractors, and horseshoes
Kenneth Allen, David DeMark, and Clayton Petsche
Research in Number Theory, Vol. 4 Issue 1 (2018) (journal) (arxiv)
- Energy integrals and small points for the Arakelov height
Paul Fili, Clayton Petsche, and Igor Pritsger
Archiv der Mathematik, Vol. 109 (2017), 441–454 (journal) (arxiv)
- A p-adic Perron-Frobenius theorem
Robert Costa, Patrick Dynes, and Clayton Petsche
Acta Arithmetica Vol. 174 (2016), 175-188 (journal) (arxiv)
- On the distribution of orbits in affine varieties
Clayton Petsche
Ergodic Theory and Dynamical Systems, Vol. 35 (2015), 2231-2241 (journal) (arxiv)
- Energy integrals over local fields and global height bounds
Paul Fili and Clayton Petsche
International Mathematics Research Notices, Vol. 2015 (2015) 1278-1294 (journal) (arxiv)
- On quadratic rational maps with prescribed good reduction
Clayton Petsche and Brian Stout
Proceedings of the American Mathematical Society, Vol. 143 (2015), 1145-1158 (journal) (arxiv)
- Global minimal models for endomorphisms of projective space
Clayton Petsche and Brian Stout
Journal de Théorie des Nombres de Bordeaux, Vol. 26 no. 3 (2014), p. 813-823 (journal) (arxiv)
- Critically separable rational maps in families
Clayton Petsche
Compositio Mathematica, Vol. 148, Iss. 06 (2012), 1880-1896 (journal) (arxiv)
- A dynamical pairing between two rational maps
Clayton Petsche, Lucien Szpiro, and Thomas J. Tucker
Transactions of the American Mathematical Society, Vol. 364 (2012), 1687-1710 (journal) (arxiv)
- A criterion for weak convergence on Berkovich projective space
Clayton Petsche
Mathematische Annalen, Vol. 348 Iss. 2 (2010) 449-465 (journal) (arxiv)
- Isotriviality is equivalent to potential good reduction for endomorphisms of PN over function fields
Clayton Petsche, Lucien Szpiro and Michael Tepper
Journal of Algebra, Vol. 322 Iss. 9 (2009) 3345-3365 (journal) (arxiv)
- Non-archimedean equidistribution on elliptic curves with global applications
Clayton Petsche
Pacific Journal of Mathematics, Vol. 242 No. 2 (2009) 345-375 (journal) (arxiv)
- S-integral preperiodic points for dynamical systems over number fields
Clayton Petsche
Bulletin of the London Mathematical Society, Vol. 40 No. 5 (2008) 749-758 (journal) (arxiv)
- Small rational points on elliptic curves over number fields
Clayton Petsche
New York Journal of Mathematics, Vol. 12 (2006) 257-268 (journal) (arxiv)
- Global discrepancy and small points on elliptic curves
Matthew Baker and Clayton Petsche
International Mathematics Research Notices, Vol. 61 (2005) 3791-3834 (journal) (arxiv)
- A quantitative version of Bilu's equidistribution theorem
Clayton Petsche
International Journal of Number Theory, 1 (2) 2005, 281-291 (journal)
Unpublished Article:
- The height of algebraic units in local fields
Clayton Petsche
Preprint (2003) (pdf)
Doctoral Dissertation:
- The distribution of Galois orbits of low height
Clayton Petsche
Advisor: Jeffrey Vaaler
The University of Texas at Austin (2003) (UT Library)
Ph.D. Advisees:
- Peter Oberly (current)
- Chatchai Noytaptim (current)
- Chifan Leung (current)
- Naveen Somasunderam (2019)
- Emerald Stacy (2018)
- Brian Stout (2013)
M.S. Advisees:
- Peter Oberly (2022)
- Naveen Somasunderam (2016)
- Jesse Andrews (2016)
- Evan Hedlund (2015)
- Emerald Stacy (2015)
- Jeff Monroe (2014)
- Jason McClelland (2014)
Links: