منابع مشابه
Absolute Derivations and Zeta Functions
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...
متن کاملComment 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.
متن کاملA Note on Absolute Derivations and Zeta Functions
This note 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.
متن کاملZeta Functions
We review various periodic orbit formulae for the zeta function whose zeros represent semiclassical approximations to the energy levels of chaotic systems. In particular, we focus on the Riemann-Siegel-resummed expression. The emphasis is on the ability of such formulae to reproduce the analytic properties of the spetral determinant, whose zeros are the exact quantum levels. As an example, the ...
متن کاملZeta Functions and Chaos
This paper is an expanded version of lectures given at M.S.R.I. in June of 2008. It provides an introduction to various zeta functions emphasizing zeta functions of a finite graph and connections with random matrix theory and quantum chaos. Section 2. Three Zeta Functions For the number theorist, most zeta functions are multiplicative generating functions for something like primes (or prime ide...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2008
ISSN: 0386-2194
DOI: 10.3792/pjaa.84.138