scholarly journals Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields

2007 ◽  
Vol 310 (2) ◽  
pp. 775-792 ◽  
Author(s):  
Kirsten Eisenträger
Keyword(s):  
Function Fields ◽  
Number Fields ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem

scholarly journals Defining Integers

2011 ◽  
Vol 17 (2) ◽  
pp. 230-251 ◽  
Author(s):  
Alexandra Shlapentokh
Keyword(s):  
North American ◽  
Number Fields ◽  
Rational Numbers ◽  
Plenary Talk ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem ◽  
Rings Of Integers ◽  
Recent Developments ◽  
University Of Notre Dame ◽  
The University

AbstractThis paper surveys the recent developments in the area that grew out of attempts to solve an analog of Hilbert's Tenth Problem for the field of rational numbers and the rings of integers of number fields. It is based on a plenary talk the author gave at the annual North American meeting of ASL at the University of Notre Dame in May of 2009.

Existential definability with bounds on archimedean valuations

2003 ◽  
Vol 68 (3) ◽  
pp. 860-878 ◽  
Author(s):  
Alexandra Shlapentokh
Keyword(s):  
Real Number ◽  
Number Fields ◽  
Algebraic Integers ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem ◽  
Rings Of Algebraic Integers

AbstractWe show that a solution to Hilbert's Tenth Problem in the rings of algebraic integers and bigger subrings of number fields where it is currently not known, is equivalent to a problem of bounding archimedean valuations over non-real number fields.

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