Publications and Preprints

The errata typically refer to the published version as the arXiv upload is updated.
  1. Elena Fuchs, Holley Friedlander, Piper Harris, Catherine Hsu, James Rickards, Katherine Sanden, Damaris Schindler, and Katherine E. Stange
    Prime and thickened prime components in Apollonian circle packings
    Accepted to Proceedings of Women in Number Theory VI. (arXiv | code )
  2. James Rickards and Katherine E. Stange
    Reciprocity obstructions in semigroup orbits in SL(2, Z)
    Submitted (arXiv | code )
  3. Summer Haag, Clyde Kertzer, James Rickards, and Katherine E. Stange
    The local-global conjecture for Apollonian circle packings is false
    Annals of Mathematics (2) 200(2): 749-770 (September 2024) (journal | arXiv | code 1 | code 2 | Quanta article | talk)
  4. James Rickards
    The Apollonian staircase
    International Mathematics Research Notices, Volume 2024, Issue 2, January 2024, Pages 1340–1372 (journal | arXiv | code)
  5. James Rickards
    Improved computation of fundamental domains for arithmetic Fuchsian groups
    Mathematics of Computation 91 (2022), no. 338, 2929-2954 (journal | arXiv | code | talk 1 | talk 2)
  6. James Rickards
    Hecke operators acting on optimal embeddings in indefinite quaternion algebras
    Acta Arithmetica 204 (2022), no. 4, pp. 347-367 (journal | arXiv | code)
  7. James Rickards
    Counting intersection numbers of closed geodesics on Shimura curves
    Research in Number Theory 9 (2023), no. 2, Paper No. 20, 45 pp.(journal | errata | arXiv | code)
  8. James Rickards
    Computing intersections of closed geodesics on the modular curve
    Journal of Number Theory 225 (2021), pp. 374-408 (journal | errata | arXiv | code)
  9. James Rickards
    When is a Polynomial a Composition of Other Polynomials?
    American Mathematical Monthly, 118 (2011), no. 4, pp. 358-363 (journal)

Other Writing