{"docId":2635,"paperId":2635,"url":"https:\/\/hrj.episciences.org\/2635","doi":"10.46298\/hrj.2017.2635","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":161,"name":"Volume 39 - 2016"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01425555","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01425555v1","dateSubmitted":"2017-01-09 13:39:36","dateAccepted":"2017-01-09 14:33:15","datePublished":"2017-01-09 14:33:26","titles":{"en":"Sieve functions in arithmetic bands"},"authors":["Coppola, Giovanni","Laporta, Maurizio"],"abstracts":{"en":"An arithmetic function f is a sieve function of range Q, if its Eratosthenes transform g = f * \u00b5 is supported in [1, Q]\u2229N, where g(q) \u03b5 q \u03b5 , \u2200\u03b5 > 0. Here, we study the distribution of f over the so-called short arithmetic bands 1\u2264a\u2264H {n \u2208 (N, 2N ] : n \u2261 a (mod q)}, with H = o(N), and give applications to both the correlations and to the so-called weighted Selberg integrals of f , on which we have concentrated our recent research."},"keywords":[{"en":"mean squares"},{"en":"arithmetic progressions"},{"en":"short intervals "},"Mathematics Subject Classification 11N37","[MATH] Mathematics [math]"]}