相关论文: Numerology

Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.

We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian…

This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…

Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…

We give some new relations for Newman digit sums respectively different modulos and put some problems. In particular, for the odd prime modulos we put an important conjecture.

This note surveys how the exterior algebra and deformations or quotients of it, gives rise to centrally important notions in five domains of mathematics: Combinatorics, Topology, Lie theory, Mathematical physics, and Algebraic geometry.

We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…

The $abc$ conjecture is a very deep concept in number theory with wide application to many areas of number theory. In this article we introduce the conjecture and give examples of its applications. In particular we apply the $abc$…

The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…

We survey large value problems, including the large value problem for Dirichlet polynomials, the restriction problem, and problems from computer science. We describe known techniques and open problems, drawing on perspectives from all three…

We consider compositions of natural numbers when there are different types of each natural number. Several recursions as well as some closed formulas for the number of compositions is derived. We also find its relationships with some known…

Prime numbers have attracted the attention of mathematiciansand enthusiasts for millenniums due to their simple definition and remarkable properties. In this paper, we study primorial numbers (the product of the first prime numbers) to…

In this paper a small survey is presented on eighteen new functions and four new sequences, such as: Inferior/Superior f-Part, Fractional f-Part, Complementary function with respect with another function, S-Multiplicative, Primitive…

We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…

In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…

A graph $G$ is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of…

We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…

Harmonic numbers are important in a lot of branches of number theory. By means of the derivative operator, the integral operator, and several summation and transformation formulas for hypergeometric series, we prove four series containing…