Sieve Functions in Arithmetic Bands,II |
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Authors: | Giovanni Coppola Maurizio Laporta |
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Institution: | 1.Avellino (AV),Italy;2.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”,Università degli Studi di Napoli “Federico II”,Napoli (NA),Italy |
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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. |
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