论文标题
Fermat-Wilson超级企业，算术衍生物和奇怪的因素化
Fermat-Wilson Supercongruences, arithmetic derivatives and strange factorizations
论文作者
论文摘要
在[THA15]中，我们查看了两个（“乘法”和“ carlitz-drinfeld添加剂”）类似物，对于Fermat和Wilson的众所周知的基本一致性，在有限领域的多项式中。当我们查看它们的素数更高的力量，即在“超级企业”上，我们发现有趣的关系将它们联系在一起，并将它们与算术衍生物和Zeta值联系起来。在当前的工作中，我们更系统地扩展了第一个模拟和与算术衍生物的连接，从而提供了许多等效的条件，将两者连接起来，现在也使用“混合衍生物”。我们还观察并证明并证明了涉及一些基本数量功能场算术的衍生条件的显着质量因素化。
In [Tha15], we looked at two (`multiplicative' and `Carlitz-Drinfeld additive') analogs each, for the well-known basic congruences of Fermat and Wilson, in the case of polynomials over finite fields. When we look at them modulo higher powers of primes, i.e. at `supercongruences', we find interesting relations linking them together, as well as linking them with arithmetic derivatives and zeta values. In the current work, we expand on the first analog and connections with arithmetic derivatives more systematically, giving many more equivalent conditions linking the two, now using `mixed derivatives' also. We also observe and prove remarkable prime factorizations involving derivative conditions for some fundamental quantities of the function field arithmetic.
