English

Smooth-supported multiplicative functions in arithmetic progressions beyond the $x^{1/2}$-barrier

Number Theory 2017-12-06 v2

Abstract

We show that smooth-supported multiplicative functions ff are well-distributed in arithmetic progressions a1a21(modq)a_1a_2^{-1} \pmod q on average over moduli qx3/5εq\leq x^{3/5-\varepsilon} with (q,a1a2)=1(q,a_1a_2)=1.

Cite

@article{arxiv.1704.04831,
  title  = {Smooth-supported multiplicative functions in arithmetic progressions beyond the $x^{1/2}$-barrier},
  author = {Sary Drappeau and Andrew Granville and Xuancheng Shao},
  journal= {arXiv preprint arXiv:1704.04831},
  year   = {2017}
}

Comments

23 pages

R2 v1 2026-06-22T19:18:43.676Z