Preprints

1. Nathan C. Ryan, Computing the Satake $p$-parameters of Siegel modular forms. Unpublished notes.
   
2. David W. Farmer, Sharon Garthwaite, Nathan C. Ryan, Ralf Schmidt, "Finding and verifying the functional equation for high degree Euler-products". Submitted.
   
3. Nathan C. Ryan, Bryan Ward*, Ryan Ward*, "Some conjectures on the maximal height of divisors of x^n-1". In preparation.
   
4. David W. Farmer, Mike Lengel*, Nathan C. Ryan, "Optimal computations of high degree L-functions". In preparation.
   
5. Nathan C. Ryan, Nils-Peter Skoruppa, Fredrik Stroemberg, "On the Rankin Convolution of Siegel Modular Forms of Degree Two". In preparation.
   
6. Nathan C. Ryan, Nils-Peter Skoruppa, "On computing odd weight Siegel modular forms of Degree 2". In preparation.
   

Recent Papers

1. Carl Pomerance and Nathan C. Ryan, The maximal height of divisors of x^n-1. Illinois J. Math. 51 (2007), no. 2, 597--604
   
2. Nathan C. Ryan and Thomas R. Shemanske, Inverting the Satake Map for Sp_n and Applications to Hecke Operators. Ramanujan J. 17 (2008), no. 2, 219--244.
   
3. Eric Bach and Nathan C. Ryan, Computational Complexity of Tunnell's Criterion Japan J. Indust. Appl. Math. 24 (2007), no. 3, 229--239.
   
4. Cris Poor, Nathan C. Ryan, David Yuen, "Lifting Puzzles in Degree 4" (Accepted for publication in the Bulletin of the Australian Math Society).
   
5. Nathan C. Ryan, "Siegel Modular Forms in Sage" (Accepted for publication in the ACM Communications in Computer Algebra)

Undergraduate Research Projects

1. Kevin McGoldrick verified the Sato-Tate conjecture for Siegel modular forms of degree 2.
2. Lauren Grainer verified the Riemann Hypothesis for spinor L-function associated to Siegel modular forms.

Sage is a far-ranging, free, open source computer algebra system in which I am pretty heavily involved. The algorithms I am developing in my research are awaiting implementation in Sage.

Code Written

1. A class that provides degree 2 Siegel modular forms and their Hecke theory for SAGE (co-written with Craig Citro and Nils-Peter Skoruppa)