On a p-adic analogue of Shintani's formula
On a p-adic analogue of Shintani's formula
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DOI：
10.1215/kjm/1250282969
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发表时间：
2005-03
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通讯作者：
Tomokazu Kashio
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文献类型：
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作者：
Tomokazu Kashio
Shintani用多重Gamma函数表示了代数数域的部分Gamma函数在s = 0处的一阶导数。Cassou-Nogu`es构造了一个p-adic模拟的偏导数函数，并计算了导数在s = 0。在本文中，我们将定义多重伽玛函数的p -adic模拟，并给出Shintani公式的p -adic模拟。该公式与原Shintani公式有很强的互补性。利用这个公式，我们得到了关于p进L -函数在s = 0处的阶的Gross猜想的一个部分结果.
Shintani expressed the first derivative at s = 0 of a partial ζ function of an algebraic number field in terms of the multiple gamma function. Cassou-Nogu`es constructed a p -adic analogue of the partial ζ -function and calculated the derivative at s = 0. In this paper, we will define a p -adic analogue of the multiple gamma function and give a p -adic analogue of Shintani’s formula. This formula has a strong resem-blance to the original Shintani’s formula. Using this formula, we get a partial result toward Gross’ conjecture concerning the order at s = 0 of the p -adic L -function.