The distribution of d4(n) in arithmetic progressions
Abstract
In this paper, we use the Petrow–Young [I. Petrow and M. P. Young, The Weyl bound for Dirichlet L-functions of cube-free conductor, Ann. Math. 192 (2020) 437–486] subconvexity bound for Dirichlet L-functions to show that [Formula: see text] has exponent of distribution [Formula: see text] when we allow an average over a mod q, thereby giving an equidistribution result for [Formula: see text] which goes past the [Formula: see text] barrier for the first time.
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Advanced Mathematical Identities
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 22
- Issue
- 08
- Pages
- 1745–1763
- Publication date
- 21 April 2026
- Language
- EN