Work

On Ramanujan expansions and primes in arithmetic progressions

Year: 2024

Type: article

Abstract: 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.

Source: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

DOI: 10.1007/s12188-024-00282-4

Author: Maurizio Laporta

Institution: University of Naples Federico II

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Università degli Studi di Napoli Federico II