Major arcs and moments of arithmetical sequences

2016/11/24 by Régis de la Bretèche, de la Bretèche, Régis, Daniel Fiorilli +1
Computer Science · Mathematics · #11B25 #11K65 #11P55 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B25 #msc:11K65 #msc:11P55 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1611.08312

27 pages

arxiv created 2016/11/24 · openalex publication_date 2016/11/24 · arxiv updated 2016/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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.

Related

• Formulas for moments of class numbers in arithmetic progressions
• Estimates for smooth Weyl sums on major arcs
• On arithmetic progressions in Lucas sequences
• Moments of moments of primes in arithmetic progressions
• On Linear Recursive Sequences with Coefficients in Arithmetic-Geometric Progressions