p-adic Taylor Polynomials
p-adic Taylor Polynomials
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p进泰勒多项式
DOI：
10.1016/j.indag.2015.12.003
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通讯作者：
E. Nagel
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文献类型：
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作者：
E. Nagel
对于实数r≥0，我们通过函数的泰勒多项式展开式的收敛来定义函数在p-进向量空间上的r-重可微性，并将该可微性定义与教科书上的定义p-进可微的迭代除差法(80‘S)进行了比较。这一比较适用于最近由GL2(K)上的p-进朗兰兹规划引出的p-进数域K上的r-重可微的定义，得到了这个可微条件等价于K上的除法差作为Q上的向量空间.
For a real number r≥ 0, we define r-fold differentiability of a function on a p-adic vector space by the convergence of its Taylor polynomial expansion, and compare this differentiability definition with that by iterated divided differences, the textbook approach (from the 80’s) to define p-adic differentiability. This comparison applies to a recent definition of r-fold differentiability over a p-adic number field K that arises from the p-adic Langlands program over GL 2 (K); yielding that this differentiability condition is equivalent to that via divided differences on K as vector space over Q p.