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

abstract

• 2018, SpringerNature. We make a detailed account of sign-normalized rank1 Drinfeld A-modules, forA 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 AndersonThakur function. We also give a new proof of a log-algebraicity theorem of Anderson.

authors

• Papanikolas, Matthew

published proceedings

• RESEARCH IN THE MATHEMATICAL SCIENCES

author list (cited authors)

• Green, N., & Papanikolas, M. A.

citation count

• 12

complete list of authors

• Green, Nathan||Papanikolas, Matthew A

publication date

• March 2018

publisher

• Springer Nature  Publisher

published in

• Research in the Mathematical Sciences  Journal

keywords

• Anderson Generating Functions
• Drinfeld Modules
• Log-algebraicity
• Pellarin L-series
• Reciprocal Sums
• Shtuka Functions

Digital Object Identifier (DOI)

• 10.1007/s40687-018-0122-8

start page

• 4

volume

• 5

issue

• 1

URL

• http://dx.doi.org/10.1007/s40687-018-0122-8