Hecke $L$-series for Sinha modules
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912468279754752 |
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| author | Davis, Erik Papanikolas, Matthew |
| author_facet | Davis, Erik Papanikolas, Matthew |
| contents | We investigate Goss $L$-functions associated to Anderson $t$-modules defined by Sinha having complex multiplication by Carlitz cyclotomic fields. We show that these $t$-modules are defined over the cyclotomic field and that their $L$-functions are products of Hecke $L$-series for Anderson's Hecke character defined via Coleman functions. Applying identities of Fang and Taelman, we prove that special values of these $L$-functions are expressible in terms of products of values of Thakur's geometric $Γ$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hecke $L$-series for Sinha modules Davis, Erik Papanikolas, Matthew Number Theory 11M38 (Primary), 11G09, 11G15, 11R60 (Secondary) We investigate Goss $L$-functions associated to Anderson $t$-modules defined by Sinha having complex multiplication by Carlitz cyclotomic fields. We show that these $t$-modules are defined over the cyclotomic field and that their $L$-functions are products of Hecke $L$-series for Anderson's Hecke character defined via Coleman functions. Applying identities of Fang and Taelman, we prove that special values of these $L$-functions are expressible in terms of products of values of Thakur's geometric $Γ$-function. |
| title | Hecke $L$-series for Sinha modules |
| topic | Number Theory 11M38 (Primary), 11G09, 11G15, 11R60 (Secondary) |
| url | https://arxiv.org/abs/2507.04113 |