The prime number theorem for random sequences
نویسندگان
چکیده
منابع مشابه
The 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 ...
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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 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 ...
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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 کاملNote on the Prime Number Theorem
Proof. First of all, we prove that if pn is the nth prime number then we have that pn ≤ 2 n−1 . Since there must be some pn+1 dividing the number p1p2 · · · pn− 1 and not exceeding it, it follows from the induction step that pn+1 ≤ 2 0 2 1 · · · 22n−1 = 220+21+···+2n−1 ≤ 22n . If x ≥ 2 is some real number, then we select the largest natural number n satisfying 22n−1 ≤ x, so that we have that 2 ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1976
ISSN: 0022-314X
DOI: 10.1016/0022-314x(76)90084-6