论文信息 - Efficient computation of p-adic heights

Efficient computation of p-adic heights

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.

David Harvey

[1] Joseph F. Traub. Analytic Computational Complexity , 1976 .

[2] K. Kedlaya. Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology , 2001, math/0105031.

[3] David Harvey,et al. Kedlaya's Algorithm in Larger Characteristic , 2006 .

[4] H. T. Kung,et al. Fast Algorithms for Manipulating Formal Power Series , 1978, JACM.

[5] Joseph H. Silverman,et al. The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[6] William Stein,et al. Computation of p-Adic Heights and Log Convergence , 2006 .

[7] S. Lang,et al. Elliptic Curves: Diophantine Analysis , 1978 .

[8] B. Mazur,et al. The $p$-adic sigma function , 1991 .

[9] K. Roberts,et al. Thesis , 2002 .

[10] D. J. Bernstein. Fast multiplication and its applications , 2008 .

[11] David Joyner,et al. SAGE: system for algebra and geometry experimentation , 2005, SIGS.