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:

Clayton Petsche and Emerald Stacy, A dynamical construction of small totally p-adic algebraic numbers, to appear in Journal of Number Theory  (arxiv)

Clayton Petsche, Attractors associated to a family of hyperbolic p-adic plane automorphisms, submitted for publication  (arxiv)

Clayton Petsche and Jeffrey D. Vaaler, A Dirichlet approximation theorem for group actions, to appear in Functiones et Approximatio Commentarii Mathematici (journal) (arxiv)

Kenneth Allen, David DeMark, and Clayton Petsche, Non-Archimedean Hénon maps, attractors, and horseshoes, Research in Number Theory, Vol. 4 Issue 1 (2018) (journal) (arxiv)

Paul Fili, Clayton Petsche, and Igor Pritsger, Energy integrals and small points for the Arakelov height, Archiv der Mathematik, Vol. 109 (2017), 441–454 (journal) (arxiv)

Robert Costa, Patrick Dynes, and Clayton Petsche, A p-adic Perron-Frobenius theorem, Acta Arithmetica Vol. 174 (2016), 175-188  (journal) (arxiv)

Clayton Petsche, On the distribution of orbits in affine varieties, Ergodic Theory and Dynamical Systems, Vol. 35 (2015), 2231-2241  (journal) (arxiv)

Paul Fili and Clayton Petsche, Energy integrals over local fields and global height bounds, International Mathematics Research Notices, Vol. 2015 (2015) 1278-1294 (journal) (arxiv)

Clayton Petsche and Brian Stout, On quadratic rational maps with prescribed good reduction, Proceedings of the American Mathematical Society, Vol. 143 (2015), 1145-1158 (journal) (arxiv)

Clayton Petsche and Brian Stout, Global minimal models for endomorphisms of projective space, Journal de Théorie des Nombres de Bordeaux, Vol. 26 no. 3 (2014), p. 813-823 (journal) (arxiv)

Clayton Petsche, Critically separable rational maps in families, Compositio Mathematica, Vol. 148, Iss. 06 (2012), 1880-1896 (journal) (arxiv)

Clayton Petsche, Lucien Szpiro, and Thomas J. Tucker, A dynamical pairing between two rational maps, Transactions of the American Mathematical Society, Vol. 364 (2012), 1687-1710 (journal) (arxiv)

Clayton Petsche, A criterion for weak convergence on Berkovich projective space, Mathematische Annalen, Vol. 348 Iss. 2 (2010) 449-465 (journal) (arxiv)

Clayton Petsche, Lucien Szpiro and Michael Tepper, Isotriviality is equivalent to potential good reduction for endomorphisms of PN over function fields, Journal of Algebra, Vol. 322 Iss. 9 (2009) 3345-3365 (journal) (arxiv)

Clayton Petsche, Non-archimedean equidistribution on elliptic curves with global applications, Pacific Journal of Mathematics, Vol. 242 No. 2 (2009) 345-375 (journal) (arxiv)

Clayton Petsche, S-integral preperiodic points for dynamical systems over number fields, Bulletin of the London Mathematical Society, Vol. 40 No. 5 (2008) 749-758 (journal) (arxiv)

Clayton Petsche, Small rational points on elliptic curves over number fields, New York Journal of Mathematics, Vol. 12 (2006) 257-268 (journal) (arxiv)

Matthew Baker and Clayton Petsche, Global discrepancy and small points on elliptic curves, International Mathematics Research Notices, Vol. 61 (2005) 3791-3834 (journal) (arxiv)

Clayton Petsche, A quantitative version of Bilu's equidistribution theorem, International Journal of Number Theory, 1 (2) 2005, 281-291 (journal)

 

Unpublished Article:

Clayton Petsche, The height of algebraic units in local fields, Preprint (2003) (pdf)

 

Doctoral Dissertation:

Clayton Petsche, The distribution of Galois orbits of low height, Advisor: Jeffrey Vaaler, The University of Texas at Austin (2003) (UT Library)

 

Ph.D. Advisees:

Naveen Somasunderam (current)
Jesse Andrews (current)
Emerald Stacy (2018)
Brian Stout (CUNY Graduate Center 2013)

 

M.S. Advisees:

Naveen Somasunderam (2016)
Jesse Andrews (2016)
Evan Hedlund (2015)
Emerald Stacy (2015)
Jeff Monroe (2014)
Jason McClelland (2014)

  

Links:

The Number Theory Group at OSU

Oregon Number Theory Days

The Number Theory Seminar at OSU

The REU Program in Mathematics and Computer Science at OSU