Kurokawa, Nobushige; Ochiai, Hiroyuki; Wakayama, Masato

Absolute derivations and zeta functions

Doc. Math. (Bielefeld) Extra Vol. Kazuya Kato's Fiftieth Birthday, 565-584 (2003)


Just as the function ring case we expect the existence of the coefficient field for the integer ring. Using the notion of one element field in place of such a coefficient field, we calculate absolute derivations of arithmetic rings. Notable examples are the matrix rings over the integer ring, where we obtain some absolute rigidity. Knitting up prime numbers via absolute derivations we speculate the arithmetic landscape. Our result is only a trial to a proper foundation of arithmetic.

Mathematics Subject Classification

11M36, 14G10, 11R42