Sigma Zeta

Zeta 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 ...

Zeta Strings

We introduce nonlinear scalar field models for open and openclosed strings with spacetime derivatives encoded in the operator valued Riemann zeta function. The corresponding two Lagrangians are derived in an adelic approach starting from the exact Lagrangians for effective fields of p-adic tachyon strings. As a result tachyons are absent in these models. These new strings we propose to call zet...

Zeta-Dimension

The zeta-dimension of a set A of positive integers is Dimζ(A) = inf{s | ζA(s) < ∞}, where ζA(s) = ∑ n∈A n. Zeta-dimension serves as a fractal dimension on Z that extends naturally and usefully to discrete lattices such as Z, where d is a positive integer. This paper reviews the origins of zeta-dimension (which date to the eighteenth and nineteenth centuries) and develops its basic theory, with ...

Generalized sigma-derivation on Banach algebras

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS