Special L-values and shtuka functions for Drinfeld modules on elliptic curves Academic Article uri icon

abstract

  • © 2018, SpringerNature. We make a detailed account of sign-normalized rank 1 Drinfeld A-modules, for A the coordinate ring of an elliptic curve over a finite field, in order to provide a parallel theory to the Carlitz module for Fq[t]. Using precise formulas for the shtuka function for 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 result prove special value formulas for Pellarin L-series in terms of an Anderson–Thakur function. We also give a new proof of a log-algebraicity theorem of Anderson.

author list (cited authors)

  • Green, N., & Papanikolas, M. A.

citation count

  • 7

publication date

  • March 2018