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arXiv 1002.22672010-02math.GM

关于分数部分积分与素差理论

On integrals of fractional parts and the theory of prime differences

Roupam Ghosh

备注：: I have not been able to implement the intuition behind my ideas in a rigorous manner. Withdrawing due to errors in the paper

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摘要：

本文研究了给定函数的分数部分的积分，并发展了一些新的工具来理解素差的行为。我们演示了如何简单地处理一些看似困难的问题有关的素数差异。这里讨论的一些好的结果包括Cramér和$\lim \inf_{n\to\infty} d_n < \infty$关于素隙的著名猜想。基于一些简单的假设，我们已经展示了如何解决这些问题。

英文摘要：

In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime differences can be dealt with. Some, good results discussed here includes, the well know conjecture on prime gaps by Cramér and $\lim \inf_{n\to\infty} d_n < \infty$. Based on some simple assumptions, we have demonstrated how to tackle such problems.

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