Related papers: Exponential and infinitary divisors
We extend the sum-of-divisors function to the complex plane via the Gaussian integers. Then we prove a modified form of Euler's classification of odd perfect numbers.
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…
We study the joint distribution of the input sum and the output sum of a deterministic transducer. Here, the input of this finite-state machine is a uniformly distributed random sequence. We give a simple combinatorial characterization of…
An exponential polynomial is a finite linear sum of terms $P(z)e^{Q(z)}$, where $P(z)$ and $Q(z)$ are polynomials. The early results on the value distribution of exponential polynomials can be traced back to Georg P\'olya's paper published…
We consider the set of extremal points of the generalized unit ball induced by gradient total variation seminorms for vector-valued functions on bounded Euclidean domains. These are central to the understanding of sparse solutions and…
In this paper, we consider the fractional sum of the divisor functions. We can improve previous results considered by Bordell\'{e}s \cite{Bo} and Liu-Wu-Yang \cite{LWY}.
The stability of exponential bases on domains in $\R^n$ has been widely studied, with much of the research focusing on small perturbations of the phase. In this paper, we consider bases on measurable domains of the real line, and their…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for them are proved.
We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient…
We present several results that show somewhat surprising equidistribution patterns in the asymptotic behaviour of the argument of entire functions of finite order.
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissipativity of the cost function, exponential estimates for both…
We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in common with analogous formulas proved previously for other vector…
We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…