Premium
Waring's Problem in Function Fields
Author(s) -
Car Mireille
Publication year - 1994
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-68.1.1
Subject(s) - mathematics , combinatorics , function field , valuation (finance) , field (mathematics) , constant (computer programming) , function (biology) , set (abstract data type) , finite field , discrete mathematics , pure mathematics , evolutionary biology , biology , finance , computer science , economics , programming language
Let L be a function field over a constant field F q . Let S be a finite and non‐empty set of valuations of L and O S be the set of S ‐integers of L. We are interested in Waring's problem in O S . More precisely, we study the representations of b ∈ O S as a sum b = b 1 k + … + b m ksatisfying the most restrictive valuation conditions for valuations belonging to the set S , that is, such that υ( b j )⩾Int(υ( b )/ k ) for every j = 1, …, m and every υ ∈ S . For this, we use the circle method.