Nathan Ryan is an Associate Professor of Mathematics at Bucknell University.
- Foundation Seminar: Infinity and Explorations in Mathematics
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 a co-founder and 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.
- I am a councillor in the Division of Mathematics and Computer Science of the Council on Undergraduate Research.
- Together with Bucknell undergraduates, I have recently begun working on applications of GIS and social media data mining applied to health care. This work is with the Farley Health Policy Center in Denver, Colorado.
- Together with Bucknell undergraduates, I have recently begun working on applying machine learning algorithms to making predictions related to the mortality of ICU patients. This work is with the Geisinger Clinical Informatics group in Danville, Pennsylvania.
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.
- 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).