Sieve Functions in Arithmetic Bands, II

Giovanni Coppola () and Maurizio Laporta ()
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Maurizio Laporta: Università degli Studi di Napoli “Federico II”

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 2, 301-311

Abstract: Abstract An arithmetic function f is called a sieve function of range Q if its Eratosthenes transform g = f * μ is supported in [1,Q] ∩ N, where g(q) ≪ ε q ε (∀ε > 0). We continue our study of the distribution of f(n) over short arithmetic bands, n ≡ ar + b (mod q), with n ∈ (N,2N] ∩ N, 1 ≤ a ≤ H = o(N) and r,b ∈ Z such that g:c:d:(r,q) = 1. In particular, the optimality of some results is discussed.

Keywords: Eratosthenes transform; arithmetic progressions; short intervals (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0270-y

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