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Sieve functions in arithmetic bands

Abstract : An arithmetic function f is 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. Here, we study the distribution of f over the so-called short arithmetic bands 1≤a≤H {n ∈ (N, 2N ] : n ≡ a (mod q)}, with H = o(N), and give applications to both the correlations and to the so-called weighted Selberg integrals of f , on which we have concentrated our recent research.
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Submitted on : Tuesday, January 3, 2017 - 4:05:39 PM
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Giovanni Coppola, Maurizio Laporta. Sieve functions in arithmetic bands. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2017, Volume 39 - 2016, pp.21 - 37. ⟨10.46298/hrj.2017.2635⟩. ⟨hal-01425555⟩

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