On Pellarin's $L$-series
Number Theory
2014-09-30 v3
Abstract
Necessary and sufficient conditions are given for a negative integer to be a trivial zero of a new type of -series recently discovered by F. Pellarin, and it is shown that any such trivial zero is simple. We determine the exact degree of the special polynomials associated to Pellarin's -series. The theory of Carlitz polynomial approximations is developed further for both additive and -linear functions. Using Carlitz' theory we give generating series for the power sums occurring as the coefficients of the special polynomials associated to Pellarin's series, and a connection is made between the Wagner representation for and the value of Pellarin's -series at 1.
Keywords
Cite
@article{arxiv.1201.0030,
title = {On Pellarin's $L$-series},
author = {Rudolph Bronson Perkins},
journal= {arXiv preprint arXiv:1201.0030},
year = {2014}
}