Contact: nathan.ryan@bucknell.edu

github

matheducators

Office: Olin 473

Nathan Ryan is a Professor of Mathematics at Bucknell University.

- 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.

- 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).

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.

- Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás; Treneer, Stephanie. "Congruences satisfied by eta-quotients." ArXiv Version.
- Armendáriz, David; Colman, Owen; Coloma, Nicolás; Ghitza, Alexandru; Ryan, Nathan C.; Terán, Darío. "Analytic evaluation of Hecke eigenvalues for classical modular forms" ArXiv Version.
- Barquero-Sanchez, Adrian; Mantilla-Soler, Guillermo; Ryan, Nathan C. "Theta series and number fields: theorems and experiments" ArXiv Version.
- 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. - 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. - Ryan, Nathan C. "Coding and cryptography: number theory applied to three love stories." (Spanish)
*Publ. Mat. Urug.*15 (2016), 123–139. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - Ryan, Nathan C.; Tornaría, Gonzalo. "A Böcherer-type conjecture for paramodular forms."
*Int. J. Number Theory*7 (2011), no. 5, 1395–1411. ArXiv Version. - 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. - 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 - 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. - Bach, Eric; Ryan, Nathan C. "Efficient verification of Tunnell's criterion."
*Japan J. Indust. Appl. Math.*24 (2007), no. 3, 229–239. Personal version - Pomerance, Carl; Ryan, Nathan C. "Maximal height of divisors of $x^n-1$."
*Illinois J. Math.*51 (2007), no. 2, 597–604. Personal version - Ryan, Nathan C. "Satake Parameters of Siegel Modular Forms", Dartmouth College Thesis (2005).