Related papers: Fillings method in number theory
We prove an inverse ternary Goldbach-type result. Let $N$ be sufficiently large and $c>0$ be sufficiently small. If $A_1,A_2,A_3\subset [N]$ are subsets with $|A_1|,|A_2|,|A_3|\geq N^{1/3-c}$, then $A_1+A_2+A_3$ contains a composite number.…
This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one…
A new solvable many-body problem of goldfish type is identified and used to revisit the connection among two different approaches to solvable dynamical systems. An isochronous variant of this model is identified and investigated.…
We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
Hindman's celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with Menger's classic covering property. The methods…
We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing…
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
$\tau$-tilting theory can be thought of as a generalization of the classical tilting theory which allows mutations at any indecomposable summand of a support $\tau$-tilting pair. Indeed, for any algebra $\Lambda$ its tilting modules…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea…
According to the similarity theorem on the distributions of the effective prime factors and by using two-part method, Goldbach theorem and, consequently, Goldbach conjecture was proved.
In this paper, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=\bar{z}G(z)+H(z)$, where $G$ and $H$ are analytic in the unit disk $|z|<1$ with $G(0)=H(0)=0$ and $H'(0)=1$. In…
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
We introduce a new kind of Information Theory. From a finite number of local, noisy comparisons, we want to design a robust filter such that the outcome is a high ranking number, Both analytical and numerical results are encouraging and we…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…