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arXiv · 1612.08628

Sieve functions in arithmetic bands, II

Giovanni Coppola·Maurizio Laporta
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Abstract

An arithmetic function $f$ is called a $sieve$ $function$ of $range$ $Q$ if its Eratosthenes transform $g=f\astμ$ has support in $[1,Q]$, where $g(q)\ll_{\varepsilon} q^{\varepsilon}$ ($\forall\varepsilon>0$). We continue our study of the distribution of such functions over short $arithmetic$ $bands$, $n\equiv ar+b\, (\bmod\,q)$, with $1\le a\le H=o(N)$ and $r,b$ integers such that g.c.d.$(r,q)=1$. In particular, we discuss the optimality of some results.

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Giovanni Coppola, Maurizio Laporta. 2016-11-24. Sieve functions in arithmetic bands, II. https://doi.org/10.1007/s13226-018-0270-y

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