My research interests are in number theory, arithmetic geometry, and dynamical systems. For further information please click here to return to my Mathematics Department index page. 

Preprints:

Clayton Petsche and Jeffrey D. Vaaler, Noncommutative Diophantine Approximation, submitted for publication (arxiv)

Kenneth Allen, David DeMark, and Clayton Petsche, Non-Archimedean Hénon maps, attractors, and horseshoessubmitted for publication (arxiv)

Publications:

Paul Fili, Clayton Petsche, and Igor Pritsger, Energy integrals and small points for the Arakelov height, Archiv der Mathematik, to appear  (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 PetscheOn the distribution of orbits in affine varietiesErgodic Theory and Dynamical Systems, Vol. 35 (2015), 2231-2241  (journal) (arxiv)

Paul Fili and Clayton Petsche, Energy integrals over local fields and global height boundsInternational 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 spaceJournal 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 Sunderam (current)
Jesse Andrews (current)
Emerald Stacy (current)
Brian Stout (CUNY Graduate Center 2013)

 

M.S. Advisees:

Naveen Sunderam (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