Nathan C. Ryan

Photo of Nathan

Office: Olin 473

Nathan Ryan is a Professor of Mathematics at Bucknell University and an affiliate faculty member in the Latin America Studies program.


A few years ago I developed a class in Mathematical Modelling for Biologists, based on a class taught by Dorothy Wallace. The notes for this course have recently been turned into a book, co-authored with Dorothy, available from World Scientific Press.


Undergraduate research projects

If you are a Bucknell student interested in doing undergraduate research with me, please drop me a line. Usually I work with students with a strong computer science/programming background, but would be happy to work with any motivated student.

Recent projects include:

Ongoing projects include

Honors Theses

Selected Papers ( indicates undergraduate co-author)

  1. Berg, Jennifer; Ryan, Nathan C.; Young, Matthew P. "Vanishing of quartic and sextic twists of L-functions." Research in Number Theory (2024): 10(1):20.
  2. Barquero-Sanchez, Adrian; Collado-Valverde, Gabriel; Ryan, Nathan C.; Salas-Jimenez, Eduardo; Sirolli, Nicolás; Villegas-Morales, Jean Carlos. "Efficient computation of the overpartition function and applications." Journal of Mathematical Analysis and Applications (2023): 127472.
  3. Massaro, Vanessa; Dhar, Swarup; Mir, Darakhshan; Ryan, Nathan C. "Carceral algorithms and the history of control: An analysis of the Pennsylvania additive classification tool." Big Data & Society 9.1 (2022): 20539517221094002
  4. Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás; Treneer, Stephanie. "Congruences satisfied by eta-quotients." Proc. Amer. Math. Soc. 149, no. 3 (2021): 1039-1051. ArXiv Version.
  5. Armendáriz, David; Colman, Owen; Coloma, Nicolás; Ghitza, Alexandru; Ryan, Nathan C.; Terán, Darío. "Analytic evaluation of Hecke eigenvalues for classical modular forms" ArXiv Version.
  6. Barquero-Sanchez, Adrian; Mantilla-Soler, Guillermo; Ryan, Nathan C. "Theta series and number fields: theorems and experiments" Ramanujan J. (2021): 1-18 ArXiv Version.
  7. Colman, Owen; Ghitza, Alexandru; Ryan, Nathan C. "Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two". Proceedings of the Thirteenth Algorithmic Number Theory Symposium, 207–220, Open Book Ser., 2, Math. Sci. Publ., Berkeley, CA, 2019. ArXiv Version.
  8. Farmer, David W.; Pitale, Ameya; Ryan, Nathan C.; Schmidt, Ralf. "Analytic L Functions: definitions, theorems and connections". Bull. Amer. Math. Soc. (N.S.) 56 (2019), no. 2, 261–280.. ArXiv Version.
  9. Ryan, Nathan C. "Coding and cryptography: number theory applied to three love stories." (Spanish) Publ. Mat. Urug. 15 (2016), 123–139.
  10. Ryan, Nathan C.; Sirolli, Nicolás; Skoruppa, Nils-Peter; Tornaría, Gonzalo. "Computing Jacobi forms." LMS J. Comput. Math. 19 (2016), suppl. A, 205–219. ArXiv Version.
  11. Ryan, Nathan C.; Tornaría, Gonzalo. "Formulas for central values of twisted spin L-functions attached to paramodular forms. With an appendix by Ralf Schmidt". Math. Comp. 85 (2016), no. 298, 907–929. ArXiv Version.
  12. Ryan, Nathan C.; Tornaría, Gonzalo; Voight, John. "Nonvanishing of twists of L-functions attached to Hilbert modular forms." LMS J. Comput. Math. 17 (2014), suppl. A, 330–348. ArXiv Version.
  13. Farmer, David W.; Ryan, Nathan C. "Evaluating L-functions with few known coefficients." LMS J. Comput. Math. 17 (2014), no. 1, 245–258. ArXiv Version.
  14. Farmer, David W.; Pitale, Ameya; Ryan, Nathan C.; Schmidt, Ralf. "Survey article: Characterizations of the Saito-Kurokawa lifting." Rocky Mountain J. Math. 43 (2013), no. 6, 1747–1757. ArXiv Version.
  15. Ghitza, Alexandru; Ryan, Nathan C.; Sulon, David. "Computations of vector-valued Siegel modular forms." J. Number Theory 133 (2013), no. 11, 3 921–3940. ArXiv Version.
  16. Ryan, Nathan C.; Skoruppa, Nils-Peter; Strömberg, Fredrik. "Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two." Math. Comp. 81 (2012), no. 280, 2361–2376. ArXiv Version.
  17. Farmer, David W.; Ryan, Nathan C.; Schmidt, Ralf. "Testing the functional equation of a high-degree Euler product." Pacific J. Math. 253 (2011), no. 2, 349–366. ArXiv Version.
  18. Ryan, Nathan C.; Tornaría, Gonzalo. "A Böcherer-type conjecture for paramodular forms." Int. J. Number Theory 7 (2011), no. 5, 1395–1411. ArXiv Version.
  19. Ryan, Nathan C.; Ward, Bryan C.; Ward, Ryan. "Some conjectures on the maximal height of divisors of $x^n-1$." Involve 3 (2010), no. 4, 451–457. ArXiv Version.
  20. Poor, Cris; Ryan, Nathan C.; Yuen, David S. "Lifting puzzles in degree four." Bull. Aust. Math. Soc. 80 (2009), no. 1, 65–82. Personal version
  21. Ryan, Nathan C.; Shemanske, Thomas R. "Inverting the Satake map for $Sp_n$ and applications to Hecke operators." Ramanujan J. 17 (2008), no. 2, 219–244. Personal version.
  22. Bach, Eric; Ryan, Nathan C. "Efficient verification of Tunnell's criterion." Japan J. Indust. Appl. Math. 24 (2007), no. 3, 229–239. Personal version
  23. Pomerance, Carl; Ryan, Nathan C. "Maximal height of divisors of $x^n-1$." Illinois J. Math. 51 (2007), no. 2, 597–604. Personal version
  24. Ryan, Nathan C. "Satake Parameters of Siegel Modular Forms", Dartmouth College Thesis (2005).