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PreprintCC BY-NC-SA 4.0arXiv

Rational Points on Affine Varieties over Finite Fields and Polygonal Number Sequences

  • Sakshi Gupta
  • Anit Kuckian
  • Indranath Sengupta
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Abstract

Authors, in an earlier work, proved that prime power subsequences of the polygonal numbers corresponding to $4$, $6$, $8$, and $10$ arise naturally as the numbers of 𝔽q-rational points of certain double Danielewski surfaces. In this work, authors generalize the previous construction and give a new family of affine varieties over finite fields such that the number of 𝔽q-rational points of these varieties give the prime power subsequence of every polygonal number sequence.

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Cite

BibTeXRIS
BibTeX
@misc{gupta2026rational,
  title = {{Rational Points on Affine Varieties over Finite Fields and Polygonal Number Sequences}},
  author = {Sakshi Gupta and Anit Kuckian and Indranath Sengupta},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32930},
  eprint = {2610.32930},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32930},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Rational Points on Affine Varieties over Finite Fields and Polygonal Number Sequences
AU  - Sakshi Gupta
AU  - Anit Kuckian
AU  - Indranath Sengupta
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32930
UR  - https://arxiv.org/abs/2610.32930
AB  - Authors, in an earlier work, proved that prime power subsequences of the polygonal numbers corresponding to $4$, $6$, $8$, and $10$ arise naturally as the numbers of 𝔽_q-rational points of certain double Danielewski surfaces. In this work, authors generalize the previous construction and give a new family of affine varieties over finite fields such that the number of 𝔽_q-rational points of these varieties give the prime power subsequence of every polygonal number sequence.
ER  -