English

Arithmetic Progressions of Squares and Multiple Dirichlet Series

Number Theory 2025-07-28 v4

Abstract

We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to C2\mathbb{C}^2 and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on x2+y2=2x^2+y^2=2.

Cite

@article{arxiv.2007.14324,
  title  = {Arithmetic Progressions of Squares and Multiple Dirichlet Series},
  author = {Thomas A. Hulse and Chan Ieong Kuan and David Lowry-Duda and Alexander Walker},
  journal= {arXiv preprint arXiv:2007.14324},
  year   = {2025}
}

Comments

32 pages, now revised with referee comments

R2 v1 2026-06-23T17:28:12.675Z