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PreprintarXiv licencearXiv

The Arithmetic of Reducible Rank 2 Hypergeometric Motives

  • Esme Rosen
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Abstract

We study the arithmetic of the realizations for hypergeometric motives attached to 3F2(1) hypergeometric series defined over number fields, focusing on the case where the étale realization is reducible and irregular. We then use motivic techniques to prove new evaluation formulas for certain 3F2(1) series, understood as a period of the hypergeometric motive. In addition, we provide examples which are closely related to the exact values of L-functions for modular forms in special cases.

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Cite

BibTeXRIS
BibTeX
@misc{rosen2026arithmetic,
  title = {{The Arithmetic of Reducible Rank 2 Hypergeometric Motives}},
  author = {Esme Rosen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28065},
  eprint = {2609.28065},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28065},
}
RIS
TY  - UNPB
TI  - The Arithmetic of Reducible Rank 2 Hypergeometric Motives
AU  - Esme Rosen
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28065
UR  - https://arxiv.org/abs/2609.28065
AB  - We study the arithmetic of the realizations for hypergeometric motives attached to _3F_2(1) hypergeometric series defined over number fields, focusing on the case where the étale realization is reducible and irregular. We then use motivic techniques to prove new evaluation formulas for certain _3F_2(1) series, understood as a period of the hypergeometric motive. In addition, we provide examples which are closely related to the exact values of L-functions for modular forms in special cases.
ER  -