MSRI 2006 Summer Graduate Workshop in Computational Number Theory
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L-series of elliptic curve of rank 2
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Each project will involve a combination of:
- Understanding and explaining the theory,
- Improving the (best-known) relevant algorithms,
- Analyzing the theoretical complexity of relevant
algorithms,
- Implementing algorithms in SAGE,
- Improving / auditing existing implementations.
General Projects
- Arithmetic in quaternion algebras (Kohel)
- Quaternion algebras over totally real fields (Dembele, Kohel)
- Mestre method of graphs (Kohel, Stein)
- Modular symbols mod p (Stein, Wiese)
- Linear algebra algorithms relevant to computing modular forms (Stein)
- Modular symbols for [specific higher-rank group] (Gunnells)
- Databases: Design the ultimate database(s) of modular forms (Stein, Kohel,
Dembele, Gunnells)
- p-adic modular forms (Wiese, Stein)
- L-functions (Kohel, Stein)
- Serre's conjecture mod pq? (if Khare hasn't already (dis-)proved it)
- Level raising mod p2? What is the right conjecture?
- Siegel modular forms
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