Splitting Hypergeometric Functions over Roots of Unity
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914855481507840 |
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| author | McCarthy, Dermot Tripathi, Mohit |
| author_facet | McCarthy, Dermot Tripathi, Mohit |
| contents | We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of unity. We provide multiple applications of these results, including new reduction and summation formulas for finite field hypergeometric functions, along with classical analogues; evaluations of special values of these functions which apply in both the finite field and p-adic settings; and new relations to Fourier coefficients of modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting Hypergeometric Functions over Roots of Unity McCarthy, Dermot Tripathi, Mohit Number Theory Classical Analysis and ODEs 11T24, 11S80, 33E50, 33C20, 11F11, 11G05 We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of unity. We provide multiple applications of these results, including new reduction and summation formulas for finite field hypergeometric functions, along with classical analogues; evaluations of special values of these functions which apply in both the finite field and p-adic settings; and new relations to Fourier coefficients of modular forms. |
| title | Splitting Hypergeometric Functions over Roots of Unity |
| topic | Number Theory Classical Analysis and ODEs 11T24, 11S80, 33E50, 33C20, 11F11, 11G05 |
| url | https://arxiv.org/abs/2404.17678 |