Sieve functions in arithmetic bands, II

Abstract

An arithmetic function $f$ is called a $sieve$ $function$ of $range$ $Q$ if its Eratosthenes transform $g=f\ast \mu$ has support in $[1,Q]$, where $g(q){\ll }_{\epsilon }{q}^{\epsilon }$ ($\forall \epsilon >0$). We continue our study of the distribution of such functions over short $arithmetic$ $bands$, $n\equiv ar+b(\mathrm{mod}q)$, 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.

5 pages, plain TeX

References in corpus (4)

• On the error term in a Parseval type formula in the theory of Ramanujan expansions
• Finite Ramanujan expansions and shifted convolution sums of arithmetical functions
• On the error term in a Parseval type formula in the theory of Ramanujan expansions II
• A note on the exponential sums of the localized divisor functions