Some concrete aspects of Hilbert’s 17th Problem

2000 ◽  
pp. 251-272 ◽  
Author(s):  
Bruce Reznick
Keyword(s):  
17Th Problem

Smale’s 17th Problem: I

2013 ◽  
pp. 331-365
Author(s):  
Peter Bürgisser ◽  
Felipe Cucker
Keyword(s):  
17Th Problem

scholarly journals On Hilbert’s 17th problem in low degree

2017 ◽  
Vol 11 (4) ◽  
pp. 929-959 ◽  
Author(s):  
Olivier Benoist
Keyword(s):  
Low Degree ◽  
17Th Problem

scholarly journals Теорема Артина для f-колец

2015 ◽  
Author(s):  
A.G. Kusraev
Keyword(s):  
Rational Functions ◽  
Sum Of Squares ◽  
Famous Theorem ◽  
The Real ◽  
Complete Ring ◽  
Positive Polynomial ◽  
Ring Of Quotients ◽  
Real Closure ◽  
F Ring ◽  
17Th Problem

The main result states that each positive polynomial p in N variables with coefficients in a unital Archimedean f-ring K is representable as a sum of squares of rational functions over the complete ring of quotients of K provided that p is positive on the real closure of K. This is proved by means of Boolean valued interpretation of Artin's famous theorem which answers Hilbert's 17th problem affirmatively.

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