相关论文: Note on the Prime Number Theorem

An introductory review of Classical Statistical Mechanics

In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic…

We give a counting based proof of the Graham Pollak Theorem

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.

A well-known conjecture asserts that there are infinitely many primes $p$ for which $p - 1$ is a perfect square. We obtain upper and lower bounds of matching order on the number of pairs of distinct primes $p,q \le x$ for which $(p - 1)(q -…

Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes in short intervals of the type $(p,p+h]$, where $p\leq X$ is a prime number and $h=\odi{X}$. Then we will apply this to prove that for every…

We describe some studies related to the frequency of prime values of integer polynomials.

The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplifications that have been discovered since the original paper.

We explicitly construct a diffeomorphic pair (p(x),p^{-1}(x)) in terms of an appropriate quadric spline interpolating the prime series. These continuously differentiable functions are the smooth analogs of the prime series and the prime…

We use analytic combinatorics to give a direct proof of the closed formula for the generating function of $p$-Bernoulli numbers.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

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.…

We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using $\sigma$-algebras, we define what a proof of a number-theoretical statement by Language Theory means. We prove…

This 1964 paper developed as an off-shoot to the foundational query: Do we discover the natural numbers (Platonically), or do we construct them linguistically? The paper also assumes computational significance in the light of Agrawal, Kayal…

This note presents criteria in terms of Bernoulli numbers for a number to be simultaneously a Wilson prime and a Lerch prime.

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

A natural partial order on the set of prime numbers was derived by the author from the internal symmetries of the primary finite fields, independently of Ford a.a., who investigated Pratt trees for primality tests. It leads to a…

In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…

In this paper we show an index theorem for gerbes