科研之友
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摘要
Let K be a complete non-archimedean field with a discrete valuation, f is an element of K[X] a polynomial with non-vanishing discriminant, A the valuation ring of K, and m the maximal ideal of A. The first main result of this paper is are formulation of Hensel's lemma that connects the number of roots off with the number of roots of its reduction modulo a power of m. We then define a condition - regularity - that yields a simple method to compute the exact number of roots off in K. In particular, we show that regularity implies that the number of roots off equals the sum of the numbers of roots of certain binomials derived from the Newton polygon.
- 出版日期2010
