Related papers: A Tale of Three Coauthors
New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…
We augment the method of Wooley (2015) by some new ideas and in a series of results, improve his metric bounds on the Weyl sums and the discrepancy of fractional parts of real polynomials with partially prescribed coefficients. We also…
We review the history of several homological conjectures, both from a chronological and a methodological point of view.
A history of Feynman's sum over histories is presented in brief. A focus is placed on the progress of path-integration techniques for exactly path-integrable problems in quantum mechanics.
We present a natural restriction of Hindman's Finite Sums Theorem that admits a simple combinatorial proof (one that does not also prove the full Finite Sums Theorem) and low computability-theoretic and proof-theoretic upper bounds, yet…
In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the…
We use an elementary argument to prove some finite sums involving expressions of the forms $(q)_n$ and $(a;q)_n$ along with inductive formulas for some sequences.
An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We give three disjoint groups of sufficient…
We give a short proof of Belaga's result on bounds to perigees of $(3x+d)$-cycles of a given oddlength. We also reformulate the Collatz cycle conjecture which is rather a algorithmic problem into a purely arithmetic problem.
We investigate the distribution of modular inverses modulo positive integers $c$ in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepancy, thereby exhibiting some deviations from random point…
In this paper, we consider universal sums of generalized polygonal numbers. Fixing $m\in\mathbb{N}_{\geq 3}$, we show two finiteness theorems for universal sums of generalized polygonal numbers whose inputs have a restricted number $L$ of…
We establish an upper bound on the tails of a random variable that arises as a solution of a stochastic difference equation. In the non--negative case our bound is similar to a lower bound obtained by Goldie and Gr\"ubel in 1996.
We describe how finite colimits can be described using the internal lanuage, also known as the Mitchell-Benabou language, of a topos, provided the topos admits countably infinite colimits. This description is based on the set theoretic…
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…
We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor…
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
Kuzmin-Landau Lemma basic for the bound of sum of exponentials is a nice example of the arithmetization of Analysis. Here we tell the interesting story of this Lemma emphasizing Landau's best constant.
An technically interesting proof of a known theorem.
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
This article establishes a new upper bound on the function $\sigma^{*}(n)$, the sum of all coprime divisors of $n$. The article concludes with two questions concerning this function.