Thirteenth Algorithmic Number Theory Symposium ANTS-XIII
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Explicit Coleman integration in larger characteristic
Alex J. Best
Abstract: We describe a more efficient algorithm to compute p-adic Coleman integrals on odd degree hyperelliptic curves for large primes p. The improvements come from using fast linear recurrence techniques when reducing differentials in Monsky-Washnitzer cohomology, a technique introduced by Harvey [Har07] when computing zeta functions. The complexity of our algorithm is quasilinear in Sqrt(p) and is polynomial in the genus and precision. We provide timings comparing our implementation with existing approaches.
© 2017-2018 Jennifer Paulhus (with thanks to Kiran S. Kedlaya, and by extension Pierrick Gaudry and Emmanuel Thomé)