Esme Rosen

activity

20242026

collaborators

4 papers

math.NT2026

The Arithmetic of Reducible Rank 2 Hypergeometric Motives

Esme Rosen

We study the arithmetic of the realizations for hypergeometric motives attached to $_{3} F_{2} (1)$ hypergeometric series defined over number fields, focusing on the case where the éta…

math.NT2026

The Explicit Hypergeometric Modularity Method III

Brian Grove, Ling Long, Esme Rosen +1

We refine the Explicit Hypergeometric Modularity Method (EHMM) and develop a variant that applies to a broader class of hypergeometric data. As an application, we establish the mod…

math.NT2025

Modular Forms and Certain $_{2} F_{1} (1)$ Hypergeometric Series

Esme Rosen

Using the framework relating hypergeometric motives to modular forms, we define an explicit family of weight 2 Hecke eigenforms with complex multiplication. We use the theory of ${…

math.NT2024

$L$ -values of certain weight 3 Modular Forms and Transformations of Hypergeometric Series

Esme Rosen

Recently, Allen, Grove, Long, and Tu proposed an explicit Hypergeometric-Modularity method which gives a concrete link between certain hypergeometric objects and modular forms. The…

The Arithmetic of Reducible Rank 2 Hypergeometric Motives

The Explicit Hypergeometric Modularity Method III

Modular Forms and Certain 2​F1​(1) Hypergeometric Series

L-values of certain weight 3 Modular Forms and Transformations of Hypergeometric Series

Modular Forms and Certain $_{2} F_{1} (1)$ Hypergeometric Series

$L$ -values of certain weight 3 Modular Forms and Transformations of Hypergeometric Series