Related papers: On the counting function for numerical monoids
Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction…
We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X,X^{5/6}$, upto an error term of $O(X^{13/16+o(1)})$. For…
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…
We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements, and a description of its convex hull. We also study the…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
We estimate the growth of the canonical integral of Hadamard-Weierstrass of measure of finite order on the complex plane by the type of counting function or average counting function of this measure
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…
We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.
We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…
The well-known result states that the square-free counting function up to $N$ is $N/\zeta(2)+O(N^{1/2})$. This corresponds to the identity polynomial $\text{Id}(x)$. It is expected that the error term in question is…
We estimate from above and below the dimension of invariant measure for contracting-on-average iterated function systems in $\R^d$.
Let f(m,n) denote the number of relatively prime subsets of {m+1,m+2,...,n}, and let Phi(m,n) denote the number of subsets A of {m+1,m+2,...,n} such that gcd(A) is relatively prime to n. Let f_k(m,n) and Phi_k(m,n) be the analogous counting…
We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.
We present a way to normalize a combinatorial Morse function into an integer-valued canonical representative of the set of discrete Morse functions inducing a given gradient field.
In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
It is shown that monotone Boolean functions on the Boolean cube capture the expected number of primes, under he usual identification by binary expansion. This answers a question posed by G.Kalai.
We calculate the leading Weyl term of the counting function for a mono-crystalline quartz sphere. In contrast to other studies of counting functions, the anisotropy of quartz is a crucial element in our investigation. Hence, we do not…
In this short note, we have defined a new "nested square root" function which generates usual Pi number for $x=2$. We have given some useful identities and asymptotic formulas of the Pi-function.
We show that the counting function of the set of values of the Carmichael $\lambda$-function is $x/(\log x)^{\eta+o(1)}$, where $\eta=1-(1+\log\log 2)/(\log 2)=0.08607...$.