Related papers: Fillings method in number theory
We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.
We develop potential theory including a Bernstein-Walsh type estimate for functions of the form $p(z)q(f(z))$ where $p,q$ are polynomials and $f$ is holomorphic. Such functions arise in the study of certain ensembles of probability measures…
In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additional results address statements in higher order arithmetic…
We study the binary Goldbach problem with arithmetic weights attached to one of the variables.
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.
We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…
Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…
The ternary Goldbach conjecture, or three-primes problem, states that every odd number $n$ greater than $5$ can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolved until now, in spite of great progress in…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner…