相关论文: Large Numbers, the Chinese Remainder Theorem, and …
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.
We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.
It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P(n))_{ n\in \mathbb N}$ has the property that there are infinitely many prime numbers dividing at least one term of this sequence.…
In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
This paper concerns the number of lattice points in a circle.
Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our…
This paper contains some personal reflections on several computational contributions to what is now known as the "String Theory Landscape". It consists of two parts. The first part concerns the origin of big numbers, and especially the…
Work in progress concerning alternative formalizations of arithmetic.
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
This article is a part of the report for the research project ``Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)'' in 1995, supported by the National Ministry of Education. There are…
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…
The presence of large partial quotients can invalidate many classical limit theorems in the metric theory of continued fractions. A commonly employed strategy to overcome this problem is to discard the largest partial quotient when…
Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $u^2=0$, $q=p^n$, $n$ a positive integer and $p$ a prime number, are investigated. By the Chinese Remainder Theorem,…
We survey the classical results on the prime number theorem
We study a topological generalization of ideal co-maximality in topological rings and present some of its properties, including a generalization of the Chinese remainder theorem. Using the hyperspace uniformity, we prove a stronger version…
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…