On duality over a certain divided power algebra with positive characteristic
Let \(R\) be a commutative overring of the algebraic closure of the Galois field \(GF(q)\), complete with respect to a non-archimedean dense absolute value. Starting from a normed \(R\)-module \(M\) with a finite orthonormal basis, the author builds the algebra \(\text{Sym} M= \oplus \text{Sym}^nM\) and studies non-archimedean analysis on its graded dual \(A'\). The study is motivated by the Carlitz zeta function \(\zeta_A(s)\) of \(A=GF(q)[T]\) defined as the sum \(\sum_{n\in A} {1\over n^s}\) \((n\) monic) with values in the field \(GF(q) ((T^{-1}))\) of the formal Laurent series over \(GF(q)\).
scientific article; zbMATH DE number 1019706
scientific article