Efficient Computation of P-adic Heights
نویسنده
چکیده
We analyse and drastically improve the running time of the algorithm of Mazur, Stein and Tate for computing the canonical cyclotomic p-adic height of a point on an elliptic curve E/Q, where E has good ordinary reduction at p ≥ 5.
منابع مشابه
Computation of p-Adic Heights and Log Convergence
This paper is about computational questions regarding p-adic height pairings on elliptic curves over a global field K. The main stumbling block to computing them efficiently is in calculating, for each of the completions Kv at the places v of K dividing p, a single quantity: the value of the p-adic modular form E2 associated to the elliptic curve. Thanks to the work of Kedlaya et al., we offer ...
متن کاملComputation of p-Adic Heights and Log Convergence In celebration of John Coates’ 60th birthday
This paper is about computational and theoretical questions regarding p-adic height pairings on elliptic curves over a global field K. The main stumbling block to computing them efficiently is in calculating, for each of the completions Kv at the places v of K dividing p, a single quantity: the value of the p-adic modular form E2 associated to the elliptic curve. Thanks to the work of Dwork, Ka...
متن کاملOn 3-adic Heights on Elliptic Curves
In 2006, Mazur, Stein, and Tate [4] gave an algorithm for computing p-adic heights on elliptic curves E over Q for good, ordinary primes p ≥ 5. Their work makes essential use of Kedlaya’s algorithm [3], where the action of Frobenius is computed on a certain basis of the first de Rham cohomology of E, with E given by a “short” Weierstrass model. Kedlaya’s algorithm requires that the working mode...
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متن کاملEfficient Computation of Rankin p-Adic L-Functions
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تاریخ انتشار 2008