Related papers: Meissel's theorem in additive arithmetical semigro…
We improve the resolvent estimate in the Kreiss matrix theorem for a set of matrices that generate uniformly bounded semigroups. The new resolvent estimate is proved to be equivalent to Kreiss's resolvent condition, and it better describes…
In 1874, Mertens proved the approximate formula for partial Euler product for Riemann zeta function at $s=1$, which is called Mertens' theorem. In this paper, we generalize Mertens' theorem for Selberg class and show the prime number…
This paper develops a theory of polynomial maps from commutative semigroups to arbitrary groups and proves that it has desirable formal properties when the target group is locally nilpotent. We apply this theory to solve Waring's Problem…
We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension $2$.…
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…
In this paper we improve the estimate for the remainder term in the asymptotic formula concerning the circle problem in an arithmetic progression.
We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…
We give some experimental observations on the growth of the norm of certain matrices related to the Mertens function. The results obtained in these experiments convince us that linear algebra may help in the study of Mertens function and…
We use a $p$-adic analogue of the analytic subgroup theorem of W\"ustholz to deduce the transcendence and linear independence of some new classes of $p$-adic numbers. In particular we give $p$-adic analogues of results of W\"ustholz…
We are interested in formulas for the number of elements in certain classes of numerical semigroups
We study perturbations of Feller generators under `lower order terms' with measurable coefficients. We investigate which properties of the original semigroup -- such as positivity, conservativeness and the Feller property -- are passed to…
Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of…
We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…
An asymptotic formula with a square root error term is obtained for the number of elements with given trace and norm in a finite semisimple algebra over a finite field. This extends previous results from finite etale algebras (commutative…
This article considers the error term of the primes counting function. It applies some recent results on the densities of prime numbers in short intervals to derive an improvement of the error term from subexponential size to fractional…
In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.
The purpose of this paper is to revisit the proof of the Gearhardt-Pr\"uss-Hwang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on $\Vert…
The paper proves the intermediate value theorem for polynomials and power series over a valued field with divisible valuation group and infinite residue field. Some further results on the behaviour of the valuation are obtained using…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…