Absolute Derivations and Zeta Functions
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چکیده
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. 2000 Mathematics Subject Classification: 11R27, 11R42, 14G10
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Comment on: Absolute Derivations and Zeta Functions
This comment answers a question raised by Kurokawa, Ochiai and Wakayama, whether a certain operator constructed using a notion of quantum non-commutativity of primes has eigenvalues related to the Riemann zeta zeros.
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تاریخ انتشار 2003