An exact degree for multivariate special polynomials

JOURNAL OF NUMBER THEORY

卷:142

Article

Perkins, Rudolph Bronson

关键词: Special polynomials;    Function field arithmetic;    Pellarin's L-series;    Positive characteristic;   

DOI  :  10.1016/j.jnt.2014.02.022

来源: Elsevier

【 摘 要 】

We introduce certain special polynomials in an arbitrary number of indeterminates over a finite field. These polynomials generalize the special polynomials associated to the Goss zeta function and Goss-Dirichlet L-functions over the ring of polynomials in one indeterminate over a finite field and also capture the special values at non-positive integers of L-series associated to Drinfeld modules over Tate algebras defined over the same ring. We compute the exact degree in to of these special polynomials and show that this degree is an invariant for a natural action of Goss' group of digit permutations. Finally, we characterize the vanishing of these multivariate special polynomials at t(0) = 1. This gives rise to a notion of trivial zeros for our polynomials generalizing that of the Goss zeta function mentioned above. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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