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Some Infinite Families of Arithmetic Symplectic Hypergeometric Groups

  • Lal Bahadur Sahu
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Abstract

Using the idea of Venkataramana's construction of infinite families of arithmetic orthogonal hypergeometric groups, we construct some of the very first examples of infinite families of arithmetic symplectic hypergeometric groups that do NOT satisfy the arithmeticity criterion of Singh and Venkataramana. For example, we show that the hypergeometric groups associated to the pairs of polynomials (x−1)4Pm(x9) and (x4+x3+2x2+x+1)Qm(x9), where Pm and Qm are integral polynomials of degree 2m such that the corresponding pair determines a Zariski dense symplectic hypergeometric group, are arithmetic in Sp(18m+4) for any integer m∈ℕ.

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Cite

BibTeXRIS
BibTeX
@misc{sahu2026some,
  title = {{Some Infinite Families of Arithmetic Symplectic Hypergeometric Groups}},
  author = {Lal Bahadur Sahu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27701},
  eprint = {2609.27701},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27701},
}
RIS
TY  - UNPB
TI  - Some Infinite Families of Arithmetic Symplectic Hypergeometric Groups
AU  - Lal Bahadur Sahu
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27701
UR  - https://arxiv.org/abs/2609.27701
AB  - Using the idea of Venkataramana's construction of infinite families of arithmetic orthogonal hypergeometric groups, we construct some of the very first examples of infinite families of arithmetic symplectic hypergeometric groups that do NOT satisfy the arithmeticity criterion of Singh and Venkataramana. For example, we show that the hypergeometric groups associated to the pairs of polynomials (x−1)^4P_m(x^9) and (x^4+x^3+2x^2+x+1)Q_m(x^9), where P_m and Q_m are integral polynomials of degree 2m such that the corresponding pair determines a Zariski dense symplectic hypergeometric group, are arithmetic in Sp(18m+4) for any integer m∈ℕ.
ER  -