Modular Forms and Certain ₂F₁(1) Hypergeometric Series

2025/02/12 by Rosen, Esme · 1 citation
#11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.08760

Abstract

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 ₂F₁(1) hypergeometric series and Ramanujan's theory of alternative bases to compute the exact central L-value of these Hecke eigenforms in terms of special beta values. We also show the integral Fourier coefficients can be written in terms of Jacobi sums, reflecting a motivic relation between the hypergeometric series and the modular forms.

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• The Explicit Hypergeometric Modularity Method III

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