# Special L-values and shtuka functions for Drinfeld modules on elliptic curves

@article{Green2016SpecialLA,
title={Special L-values and shtuka functions for Drinfeld modules on elliptic curves},
author={Nathan Green and Matthew A. Papanikolas},
journal={Research in the Mathematical Sciences},
year={2016},
volume={5},
pages={1-47}
}
• Published 14 July 2016
• Mathematics
• Research in the Mathematical Sciences
We make a detailed account of sign-normalized rank 1 Drinfeld $$\mathbf {A}$$A-modules, for $$\mathbf {A}$$A the coordinate ring of an elliptic curve over a finite field, in order to provide a parallel theory to the Carlitz module for $$\mathbb {F}_q[t]$$Fq[t]. Using precise formulas for the shtuka function for $$\mathbf {A}$$A, we obtain a product formula for the fundamental period of the Drinfeld module. Using the shtuka function we find identities for deformations of reciprocal sums and as a…
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