Related papers: Growth function for an $n$-valued dynamics
We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question…
We study the stochastic growth process in discrete time $x_{i+1} = (1 + \mu_i) x_i$ with growth rate $\mu_i = \rho e^{Z_i - \frac12 var(Z_i)}$ proportional to the exponential of an Ornstein-Uhlenbeck (O-U) process $dZ_t = - \gamma Z_t dt +…
We construct an increasing, submultiplicative, arbitrarily rapid function which is not equivalent to the growth function of any finitely generated algebra, demonstrating the difficulty in characterizing growth functions in an asymptotic…
The growth rate function $r_N$ counts the number of irreducible representations of simple complex Lie groups of dimension $N$. While no explicit formula is known for this function, previous works have found bounds for $R_N=\sum_{i=1}^Nr_i$.…
Fixing an arithmetic lattice $\Gamma$ in an algebraic group $G$, the commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\Delta$ with $[\Gamma : \Gamma \cap \Delta] [\Delta: \Gamma \cap \Delta] =…
We are interested in the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$. This maximum is shown to be strictly increasing in terms of the number of cusps for…
This paper gives asymptotic formulas for the subgroup growth and maximal subgroup growth of all Baumslag-Solitar groups.
This paper is a sequel to "Representation growth of maximal class groups: non-exceptional primes". We use a constructive method to calculate some exceptional cases of $p$-local representation zeta functions of a family of finitely generated…
The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.
We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot groups. This class contains groups for which it is known that their Dehn function grows no faster than $n^2\log n$. We therefore…
We introduce a new method of proving upper estimates of growth of finitely generated groups and constructing groups of intermediate growth using graphs of their actions. These estimates are of the form $\exp(n^\alpha)$ for some $\alpha<1$,…
We consider the question of which semigroups can occur as the semigroup $S_R(\nu)$ of positive values of a rank 1 valuation dominating a Noetherian local ring $R$. We give a number of bounds of polynomial type on the growth of…
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
In this paper we shall consider the assymptotic growth of $|P_n(z)|^{1/k_n}$ where $P_n(z)$ is a sequence of entire functions of genus zero. Our results extend a result of J. Muller and A. Yavrian. We shall prove that if the sequence of…
The maximal normal subgroup growth type of a finitely generated group is $n^{\log n}$. Very little is known about groups with this type of growth. In particular, the following is a long standing problem: Let $\Gamma$ be a group and $\Delta$…
We define the class of groups of bounded type from tile inflations. These tile inflations also determine some automata describing the groups. In the case when the automata are stationary, we show that if the set of incompressible elements…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…
We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.
We consider growth conditions for (frequently) Birkhoff-universal functions of exponential type with respect to the different rays emanating from the origin. For that purpose, we investigate their (conjugate) indicator diagram or,…