Jacobiens，Jacobiennes et stabilité numérique
Jacobiens, jacobiennes et stabilité numérique
摘要：
本文研究了复数域上曲线的雅可比簇在亏格增长到无穷大时算术运算的复杂性和稳定性。我们专注于模曲线。模曲线的雅可比矩阵的有效和稳定的计算对于在确定性多项式时间内计算模形式的系数是有用的。这项工作是我对Edixhoven解决这个问题的计划的贡献的一部分。
英文摘要：
This paper is concerned with the complexity and stability of arithmetic operations in the jacobian variety of curves over the field of complex numbers, as the genus grows to infinity. We focus on modular curves. Efficient and stable computation in the jacobian of modular curves is useful for computing coefficients of modular forms in deterministic polynomial time. This work is part of my contribution to Edixhoven's program for solving this problem.
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