Paper detail

Major arcs and moments of arithmetical sequences

We give estimates for the first two moments of arithmetical sequences in progressions. Instead of using the standard approximation, we work with a generalization of Vaughan's major arcs approximation which is similar to that appearing in earlier work of Browning and Heath-Brown on norm forms. We apply our results to the sequence $τ_k(n)$, and obtain unconditional results in a wide range of moduli.