论文标题
关于Ramanujan扩展和算术进展的素数
On Ramanujan expansions and primes in arithmetic progressions
论文作者
论文摘要
著名的Delange定理为算术函数提供了足够的条件，即与Wintner先前结果所提供的系数相关的Ramanujan扩展的总和。通过将delange定理应用于von Mangoldt函数与其不完整形式的相关性，我们推断出涉及算术进程中质量数的计数函数的不等式。一个了不起的方面是，这种不平等等同于Hardy和Littlewood的著名猜想公式。
A celebrated theorem of Delange gives a sufficient condition for an arithmetic function to be the sum of the associated Ramanujan expansion with the coefficients provided by a previous result of Wintner. By applying the Delange theorem to the correlation of the von Mangoldt function with its incomplete form, we deduce an inequality involving the counting function of the prime numbers in arithmetic progressions. A remarkable aspect is that such an inequality is equivalent to the famous conjectural formula by Hardy and Littlewood for the twin primes.
