PreprintarXiv licencearXiv
A Hypergeometric RM Surface: Integral Monodromy and Level-11 Covers
Abstract
We study a genus-two hypergeometric family whose Jacobians have real multiplication by Q(√5). We identify the relevant primitive factor and integral rank-two monodromy; at one real embedding the projective image is Δ(2,5,∞), while the conjugate image is nondiscrete. At the primes above $11$, the degree-$12$ Borel covers are quadratic pullbacks of genus-one triangular modular curves. The same rank-two systems have finite-field hypergeometric Frobenius traces, yielding the local Euler factors and a quadratic transformation twisted by the character of $2$.
Related
- Resolving Thinness of Degree-Six Symplectic Hypergeometric Monodromy Groups
- Xiao's Genus-Two Fibration: Branched Covers and Braid Monodromy
- Double basic hypergeometric sums via a regularized Jackson q-integral
- Coxeter Symmetry in Hypergeometric Functions and Elliptic Integral Moments
- Analytical and Numerical Treatment of a Mixed Volterra–Fredholm Integral Equation of the First Kind with a Hypergeometric Kernel
BibTeX
@misc{tiwari2026hypergeometric,
title = {{A Hypergeometric RM Surface: Integral Monodromy and Level-11 Covers}},
author = {Devendra Tiwari},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07849},
eprint = {2611.07849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07849},
}
RIS
TY - UNPB
TI - A Hypergeometric RM Surface: Integral Monodromy and Level-11 Covers
AU - Devendra Tiwari
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07849
UR - https://arxiv.org/abs/2611.07849
AB - We study a genus-two hypergeometric family whose Jacobians have real multiplication by Q(√5). We identify the relevant primitive factor and integral rank-two monodromy; at one real embedding the projective image is Δ(2,5,∞), while the conjugate image is nondiscrete. At the primes above $11$, the degree-$12$ Borel covers are quadratic pullbacks of genus-one triangular modular curves. The same rank-two systems have finite-field hypergeometric Frobenius traces, yielding the local Euler factors and a quadratic transformation twisted by the character of $2$.
ER -