An arithmetic function $f$ is called a {it sieve function} of {it range} $Q$ if its Eratosthenes transform $g=fastmu$ is supported in $[1,Q]capN$, where $g(q)ll_{arepsilon} q^{arepsilon}$ ($orallarepsilon>0$). We continue our study of the distribution of $f(n)$ over short {it arithmetic bands}, $nequiv ar+b, (mod,q)$, with $nin(N,2N]capN$, $1le ale H=o(N)$ and $r,binZ$ such that ${ m g.c.d.}(r,q)=1$. In particular, the optimality of some results is discussed.
Sieve functions in arithmetic bands, II / Coppola, G.; Laporta, M.. - In: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS. - ISSN 0019-5588. - 49:2(2018), pp. 301-311. [10.1007/s13226-018-0270-y]
Sieve functions in arithmetic bands, II
Laporta M.
2018
Abstract
An arithmetic function $f$ is called a {it sieve function} of {it range} $Q$ if its Eratosthenes transform $g=fastmu$ is supported in $[1,Q]capN$, where $g(q)ll_{arepsilon} q^{arepsilon}$ ($orallarepsilon>0$). We continue our study of the distribution of $f(n)$ over short {it arithmetic bands}, $nequiv ar+b, (mod,q)$, with $nin(N,2N]capN$, $1le ale H=o(N)$ and $r,binZ$ such that ${ m g.c.d.}(r,q)=1$. In particular, the optimality of some results is discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
