# Maximal Unipotent Monodromy and p-adic Eigenvalue Formulas

“Maximal Unipotent Monodromy and p-adic Eigenvalue Formulas” (2026), by Alan Adolphson et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Alan Adolphson, Steven Sperber, Hao Zhang
- Published: November 4, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.05886
- Free PDF: https://arxiv.org/pdf/2611.05886

## Abstract

We establish p-adic formulas for the eigenvalues of Frobenius in the case of the family of hyperkloosterman sums. The deformation equation in this case has maximal unipotent monodromy, and the interplay of Frobenius and the differential equation plays an important role in establishing p-adic analytic formulas for the eigenvalues.

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