Nathan C. Ryan

Nathan Ryan is a Professor of Mathematics at Bucknell University.

Teaching

• Foundation Seminar: Infinity and Mathematical Explorations

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.

Projects

• I am trained as a computational number theorist and am most interested in computations involving modular forms and L-functions.
• I am an editor of the L-functions and Modular Database (LMFDB).
• I am an editor for Frontiers for Young Minds, a journal reviewed and read by young scientists. Write me a note if you might be interested in contributing.
• With students I work on interdisciplinary projects in applied data science. Here's a sample of these kinds of projects:
• analyzing patient flow through a hospital system using Markov models (partnered with Geisinger in Danville, PA)
• predicting onset of septic shock for septic patients (partnered with Geisinger in Danville, PA)
• determining how equitably distributed access to health care is in Colorado (partnered with Farley Health Center in Colorado)
• applying statistical techniques and data visualization techniques to eye-tracking data to study the films of Jacques Tati (partnered with Professor Faden in Film and Media Studies and Professor Mitchel in Psychology)
• analyzing Department of Corrections data to understand what factors influence parole decision (partnered with Professor Mir in Computer Science and Professor Massaro in Geography).

Students

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 program, but would be happy to work with any motivated student.

Selected Papers

1. Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás; Treneer, Stephanie. "Congruences satisfied by eta-quotients." ArXiv Version.
2. Armendáriz, David; Colman, Owen; Coloma, Nicolás; Ghitza, Alexandru; Ryan, Nathan C.; Terán, Darío. "Analytic evaluation of Hecke eigenvalues for classical modular forms" ArXiv Version.
3. Barquero-Sanchez, Adrian; Mantilla-Soler, Guillermo; Ryan, Nathan C. "Theta series and number fields: theorems and experiments" ArXiv Version.
4. Colman, Owen; Ghitza, Alexandru; Ryan, Nathan C. "Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two". To appear in Proceedings of ANTS XIII. ArXiv Version.
5. Farmer, David W.; Pitale, Ameya; Ryan, Nathan C.; Schmidt, Ralf. "Analytic L Functions: definitions, theorems and connections". To appear in Bulletin of the American Mathematical Society. ArXiv Version.
6. Ryan, Nathan C. "Coding and cryptography: number theory applied to three love stories." (Spanish) Publ. Mat. Urug. 15 (2016), 123–139.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. Ryan, Nathan C.; Tornaría, Gonzalo. "A Böcherer-type conjecture for paramodular forms." Int. J. Number Theory 7 (2011), no. 5, 1395–1411. ArXiv Version.
16. 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.
17. 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
18. 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.
19. Bach, Eric; Ryan, Nathan C. "Efficient verification of Tunnell's criterion." Japan J. Indust. Appl. Math. 24 (2007), no. 3, 229–239. Personal version
20. Pomerance, Carl; Ryan, Nathan C. "Maximal height of divisors of $x^n-1$." Illinois J. Math. 51 (2007), no. 2, 597–604. Personal version
21. Ryan, Nathan C. "Satake Parameters of Siegel Modular Forms", Dartmouth College Thesis (2005).