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PreprintCC BY 4.0arXiv

S-squareful values of binary quadratic forms

  • Sarah Sophie Pohl
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Abstract

Shute showed that the leading constant in the asymptotic formula for squareful values of the form ax2+by2 does not match with the conjecture established by Pieropan, Smeets, Tanimoto and Várilly-Alvarado. In this paper, S-squareful values of this form are considered for S the set of primes that divide a and b. We prove an asymptotic formula for these numbers and show that the leading constant of the asymptotic formula still does not match the conjecture. Furthermore, we consider the updated conjecture established by Chow, Loughran, Takloo-Bighash, and Tanimoto regarding the leading constant for Campana points in the given setting and show that this constant is consistent with our computed constant.

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Cite

BibTeXRIS
BibTeX
@misc{pohl2026ssquareful,
  title = {{S-squareful values of binary quadratic forms}},
  author = {Sarah Sophie Pohl},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20316},
  eprint = {2610.20316},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20316},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - S-squareful values of binary quadratic forms
AU  - Sarah Sophie Pohl
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20316
UR  - https://arxiv.org/abs/2610.20316
AB  - Shute showed that the leading constant in the asymptotic formula for squareful values of the form ax^2+by^2 does not match with the conjecture established by Pieropan, Smeets, Tanimoto and Várilly-Alvarado. In this paper, S-squareful values of this form are considered for S the set of primes that divide a and b. We prove an asymptotic formula for these numbers and show that the leading constant of the asymptotic formula still does not match the conjecture. Furthermore, we consider the updated conjecture established by Chow, Loughran, Takloo-Bighash, and Tanimoto regarding the leading constant for Campana points in the given setting and show that this constant is consistent with our computed constant.
ER  -