Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01425555v1

Volume: Volume 39

Published on: January 9, 2017

Submitted on: January 9, 2017

Keywords: mean squares,arithmetic progressions,short intervals ,Mathematics Subject Classification 11N37,[MATH] Mathematics [math]

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