Prime number theorem for regular Toeplitz subshifts
نویسندگان
چکیده
We prove that neither a prime nor {an l-almost prime} number theorem hold in the class of regular Toeplitz subshifts. But, {when quantitative strengthening regularity with respect to periodic structure involving Euler's totient function is assumed}, then two theorems hold.
منابع مشابه
Dirichlet Prime Number Theorem
In number theory, the prime number theory describes the asymptotic distribution of prime numbers. We all know that there are infinitely many primes,but how are they distributed? Dirichlet’s theorem states that for any two positive coprime integers a and d, there are infinitely many primes which are congruent to a modulo d. A stronger form of Dirichlet’s theorem states that the sum of the recipr...
متن کاملThe Prime Number Theorem
The Prime Number Theorem asserts that the number of primes less than or equal to x is approximately equal to x log x for large values of x (here and for the rest of these notes, log denotes the natural logarithm). This quantitative statement about the distribution of primes which was conjectured by several mathematicians (including Gauss) early in the nineteenth century, and was finally proved ...
متن کاملPrime Number Theorem Lecture Notes
The Prime Number Theorem asserts that the number of primes less than or equal to x is approximately equal to x log x for large values of x (here and for the rest of these notes, log denotes the natural logarithm). This quantitative statement about the distribution of primes which was conjectured by several mathematicians (including Gauss) early in the nineteenth century, and was finally proved ...
متن کاملPrime Number Theorem for Algebraic Function Fields
Elementary proofs of the abstract prime number theorem of the form A(w) = qm + 0(qmm~i) for algebraic function fields are given. The proofs use a refinement of a tauberian theorem of Bombieri. 0. Introduction The main purpose of this paper is to give elementary proofs of the abstract prime number theorem for algebraic function fields (henceforth, the P.N.T.) which was established in the author'...
متن کاملPrime Number Generation Based On Pocklington's Theorem
Public-key cryptosystems base their security on well-known number-theoretic problems, such as factorisation of a given number n. Hence, prime number generation is an absolute requirement. Many prime number generation techniques have been proposed up-to-date, which differ mainly in terms of complexity, certainty and speed. Pocklington’s theorem, if implemented, can guarantee the generation of a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2021
ISSN: ['0143-3857', '1469-4417']
DOI: https://doi.org/10.1017/etds.2021.3