Generalized Legendre curves and quaternionic multiplication
From MaRDI portal
Publication:898811
DOI10.1016/j.jnt.2015.04.019zbMath1336.33009arXiv1412.6906OpenAlexW1597986446MaRDI QIDQ898811
Fang-Ting Tu, Jenny G. Fuselier, Ling Long, Alyson Deines, Holly Swisher
Publication date: 21 December 2015
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1412.6906
hypergeometric functionsabelian varietiesShimura curvesGalois representationstriangle groupscounting points over finite fields
Abelian varieties of dimension (> 1) (11G10) Galois representations (11F80) Classical hypergeometric functions, ({}_2F_1) (33C05)
Related Items (7)
A whipple \(_7F_6\) formula revisited ⋮ Some supercongruences occurring in truncated hypergeometric series ⋮ Potentially 𝐺𝐿₂-type Galois representations associated to noncongruence modular forms ⋮ Appell-Lauricella hypergeometric functions over finite fields, and a new cubic transformation formula ⋮ Hypergeometric functions over finite fields ⋮ Hypergeometric functions over finite fields ⋮ A cubic transformation formula for Appell-Lauricella hypergeometric functions over finite fields
Uses Software
Cites Work
- \(p\)-adic analogues of Ramanujan type formulas for \(1/\pi\)
- Hypergeometric functions and a family of algebraic curves
- A new interpretation of the Shimura curve with discriminant 6 in terms of Picard modular forms
- Trace formulas for Hecke operators, Gaussian hypergeometric functions, and the modularity of a threefold
- Values of hypergeometric functions
- Hypergeometric series over finite fields and Apéry numbers
- Arithmetic triangle groups
- Exceptional sets of hypergeometric series.
- Triangle Fuchsian differential equations with apparent singularities
- On Atkin and Swinnerton-Dyer congruence relations. II
- On analytic families of polarized abelian varieties and automorphic functions
- Construction of class fields and zeta functions of algebraic curves
- On Atkin--Swinnerton-Dyer congruence relations
- Representations induced in an invariant subgroup
- Galois representations with quaternion multiplication associated to noncongruence modular forms
- Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves
- Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves
- HYPERGEOMETRIC FUNCTIONS OVER FINITE FIELDS AND THEIR RELATIONS TO ALGEBRAIC CURVES
- Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
- A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform
- Hypergeometric Functions Over Finite Fields
- Hypergeometric Functions, My Love
- Values of Gaussian hypergeometric series
- Hypergeometric Abelian Varieties
- Schwarzian differential equations and Hecke eigenforms on Shimura curves
- A Gaussian hypergeometric series evaluation and Apéry number congruences
- On $ℓ$-adic representations for a space of noncongruence cuspforms
- On a conjecture of hasse concerning multiplicative relations of Gaussian sums
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Generalized Legendre curves and quaternionic multiplication
