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arXiv · 2507.04113

Hecke $L$-series for Sinha modules

Erik Davis·Matthew Papanikolas
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Abstract

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 $\Gamma$-function.

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Erik Davis, Matthew Papanikolas. 2025-07-05. Hecke $L$-series for Sinha modules. https://arxiv.org/abs/2507.04113

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