From the reviews:" The book... is a thorough and very readable introduction to the arithmetic
of function fields of one variable over a finite field, by an author who has made fundamental …

A number of constructions in function field arithmetic involve extensions from linear objects
using digit expansions. This technique is described here as a method of constructing …

Call a domain D with quotient field K an interpolation domain if, for each choice of distinct
arguments a1,…, an and arbitrary values c1,…, cn in D, there exists an integer-valued …

We study the class of univariate polynomials β k (X), introduced by Carlitz, with coefficients
in the algebraic function field F q (t) over the finite field F q with q elements. It is implicit in the …

Résumé Soit D un anneau intégre de corps des fractions K. Pour tout x∈ D, on étudie
l'anneau 𝔹 x (D)={f∈ K [X]|∀ a∈ D, f (xX+ a)∈ D [X]}. Ces anneaux forment un …

The object of this paper is to identify the divided power series corresponding to the zeta
measure associated to F q [T]. The first section introduces the zeta function for F q [T] and …

We introduce two new notions of “$ P $-ordering” and use them to define a three-parameter
generalization of the usual factorial function. We then apply these notions of $ P $-orderings …

Abstract The Binomial Theorem has played a crucial role in the development of
mathematics, algebraic or analytic, pure or applied. It was very important in the development …

We describe an ultrametric version of the Stone-Weierstrass theorem, without any
assumption on the residue field. If E is a subset of a rank-one valuation domain V, we show …

Devoted to counterparts of classical structures of mathematical analysis in analysis over
local fields of positive characteristic, this book treats positive characteristic phenomena from …