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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.08760 |
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Table of Contents:
- 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 ${}_2F_1(1)$ 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.