Research

Books

  • Summing it Up: From One Plus One to Modern Number Theory, with Avner Ash. Princeton University Press, 2016. Reviews and errata.
  • Elliptic Tales: Curves, Counting, and Number Theory, with Avner Ash. Princeton University Press, 2012. Reviews and errata.
  • Fearless Symmetry: Exposing the Hidden Patterns of Numbers, with Avner Ash. Princeton University Press, 2006, paperback 2009. Reviews and errata.
  • Getting Started with Mathematica®, with C-K. Cheung, G.E. Keough, and Charles Landraitis. Wiley, 2005.
  • Contributor to Standard Mathematical Tables and Formulæ, Thirty-first Edition, Edited by Daniel Zwillinger, CRC Press, 2003, New York.
  • Contributor to Standard Mathematical Tables and Formulæ, Thirtieth Edition, Edited by Daniel Zwillinger, CRC Press, 1996, New York.

Papers

  • “Lattice Packing by Spheres and Eutactic Forms,” with Avner Ash, Experimental Mathematics, to appear. Click here for PDF format.
  • “Frequencies of Successive Pairs of Prime Residues,” with Avner Ash, Laura Beltis, and Warren Sinnott, Experimental Mathematics,  20:4, 2011, 400–411. Click here for PDF format.
  • “Frequences of Successive Tuples of Frobenius Classes,” with Avner Ash and Brandon Bate, Experimental Mathematics18:1, 2009, 55–63. Click here for PDF format.
  • “Prime Specialization in Genus 0,” with Brian Conrad and Keith Conrad, Transactions of the American Mathematical Society360:6, June, 2008, 2867–2908. Click here for PDF format.
  • “Generalized Non-abelian Reciprocity Laws: A Context for Wiles’s Proof,” with Avner Ash, Bulletin of the London Mathematical Society32, 2000: 385–397. Click here for PDF format.
  • “A Generalization of a Conjecture of Hardy and Littlewood to Algebraic Number Fields,” with John H. Smith, Rocky Mountain Journal of Mathematics30:1, Spring, 2000: 195–215. Click here for PDF format.
  • S-Integer Points on Elliptic Curves,” with Joseph SilvermanPacific Journal of Mathematics167, 1995: 263–288. Click here for PDF format.
  • “On the Integrality of Some Galois Representations,” Proceedings of the American Mathematical Society123:1, January, 1995: 299–301. Click here for PDF format.
  • “A Note on Roth’s Theorem,” Journal of Number Theory36:1, September, 1990: 127–132. Click here for PDF format.
  • “Antigenesis: A Cascade Theoretical Analysis of the Size Distribution of Antigen-Antibody Complexes: Applications of graphs in chemistry and physics,” with John Kennedy, Lou Quintas, and Martin Yarmush. Discrete Applied Mathematics, 19:1–3, 1988: 177–194.