Relative Growth Series in some Hyperbolic Groups

Some study on the growth properties of entire functions represented by vector valued Dirichlet series in the light of relative Ritt orders

For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of thei...

On Some Results in the Light of Generalized Relative Ritt Order of Entire Functions Represented by Vector Valued Dirichlet Series

In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.

RELATIVE GROWTH SERIES IN SOME HYPERBOLIC GROUPSRichard

Salem numbers and growth series of some hyperbolic graphs

Extending the analogous result of Cannon andWagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick (Floyd and Plotnick, 1994)) are reciprocal Salem polynomials. As a consequence, the growth ...

Growth Series of Some Hyperbolic Graphs and Salem Numbers

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m associated to regular tessellations of hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick [FP94]) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs a...