Related papers: The many-to-few lemma and multiple spines
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…
The main object of this paper is to find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria…
This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which…
Formulae for the number of branch points of one-dimensional orbifolds defined over a non-archimedean local field and uniformisable by discrete projective linear groups are given. They depend only on the uniformising group. The method of…
The purpose of this paper is to find an explicit formula and asymptotic estimate for the total number of sum of weighted records over set partitions of $[n]$ in terms of Bell numbers. For that we study the generating function for the number…
Introducing a notion of the weighted mean sigma-r curvature and using the weighted Newton transformations we derive in this paper some integral formulae on weighted manifolds. These formulae generalize the flux formula and some of its…
Difficult it is to formulate achievable sensitivity bounds for quantum multiparameter estimation. Consider a special case, one parameter from many: many parameters of a process are unknown; estimate a specific linear combination of these…
The general theory of the branching processes is used for establishing the relation between the parameters $k$ and $\bar n$ of the negative binomial distribution. This relation gives the possibility to describe the overall data on…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
A common approach to aggregate classification estimates in an ensemble of decision trees is to either use voting or to average the probabilities for each class. The latter takes uncertainty into account, but not the reliability of the…
Sums of the singular series constants that appear in the Hardy--Littlewood $k$-tuples conjectures have long been studied in connection to the distribution of primes. We study constrained sums of singular series, where the sum is taken over…
The first aim is to construct generalizations of Polya type point process by applying a branching mechanism to these point processes. Conditions are given under which these point processes satisfy an integration by parts formula.…
Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.
Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible…
In earlier work the authors obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here formulas are obtained for joint probabilities for several particles. In the case of a single…
Two purposes will be shown in this paper. The first one is to extend the classic Tumura-Clunie type theorem for meromorphic functions of one complex variable to meromorphic functions of several complex variables by using Clunie lemma. The…
We present some addition theorems for spin-weighted spherical harmonics, generalizing previous results for scalar (spin-zero) spherical harmonics. These addition theorems involve sums over the azimuthal quantum number of products of two…
We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the…
A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the…
We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum…