筛函数的变换

希尔伯特第八问题研究

Study on Hilbert's Eighth Problems

本文通过筛函数变换改进筛法与算术数列素数定理，宣称证明广义黎曼猜想和黎曼猜想，并改进塞尔伯格线性筛法以证明哥德巴赫猜想与孪生素数猜想，从而基本解决希尔伯特第八问题。

Sieve Procedure for the Möbius prime-functions, the Infinitude of Primes and the Prime Number Theorem

Using a sieve procedure akin to the sieve of Eratosthenes we show how for each prime $p$ to build the corresponding Möbius prime-function, which in the limit of infinitely large primes becomes identical to the original Möbius function. Discussing this limit we present two simple proofs of the Prime Number Theorem. In the framework of this approach we give several proofs of the infinitude of primes.

Dynamical Sieve of Eratosthenes

In this document, prime numbers are related as functions over time, mimicking the Sieve of Eratosthenes. For this purpose, the mathematical representation is a uni-dimentional time line depicting the number line for positive natural numbers N, where each number n represents a time t. In the same way as the Eratosthenes' sieve, which iteratively mark as composite the multiples of each prime, starting at each prime. This dynamical prime number function P(s) zero-cross all composite numbers departing from primes, following a linear progression over time.

An algorithmic implementation of the Pi function based on a new sieve

In this paper we propose an algorithm that correctly discards a set of numbers (from a previously defined sieve) with an interval of integers. Leopoldo's Theorem states that the remaining integer numbers will generate and count the complete list of primes of absolute value greater than 3 in the interval of interest. This algorithm avoids the problem of generating large lists of numbers, and can be used to compute (even in parallel) the prime counting function $π(h)$.

孪生素数问题的一种构造性启发式筛法

A Constructive Heuristic Sieve for the Twin Prime Problem

本文提出一种基于筛法理论的构造性启发式模型，通过$f(t;z)$函数分析将筛密度乘积表示为无穷级数之比，为近似Hardy-Littlewood孪生素数常数提供新路径。

Sifting Function Partition for the Goldbach Problem

All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so and which is, in general, very difficult. Some new methods introduced in this paper show that the Goldbach problem can be solved under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can be implemented by using one of the three methods called sifting function partition by integer sort, sif…