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:

  • 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: