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THE PROPORTION OF FAILURES OF THE HASSE NORM PRINCIPLE

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry Algebraic number theory: global fields Homological methods (field theory)

Published online by Cambridge University Press:  22 January 2016

T. D. Browning  and
R. Newton
T. D. Browning
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, U.K. email t.d.browning@bristol.ac.uk
R. Newton
Affiliation:
Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440 Bures-sur-Yvette, France email newton@ihes.fr
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Abstract

For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.

MSC classification

Primary: 11G35: Varieties over global fields
Secondary: 11R37: Class field theory 12G05: Galois cohomology 14G05: Rational points

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 2 , 2016 , pp. 337 - 347
Copyright
Copyright © University College London 2016 

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