eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2017-01-09
Volume 39 - 2016
10.46298/hrj.2017.2635
2635
journal article
Sieve functions in arithmetic bands
Giovanni Coppola
Maurizio Laporta
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.
https://hrj.episciences.org/2635/pdf
mean squares
arithmetic progressions
short intervals
Mathematics Subject Classification 11N37
[MATH] Mathematics [math]