On Ramanujan expansions and primes in arithmetic progressions

Autor:	Laporta, Maurizio
Rok vydání:	2022
Předmět:	Mathematics - Number Theory Primary 11N05 Secondary 11P32 11N37
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.01581 Zobrazit plný text záznamu View this record from Arxiv