scholarly journals ``Hasse principle'' for $GL_2(D)$

1999 ◽  
Vol 75 (7) ◽  
pp. 141-142 ◽  
Author(s):  
Takashi Ono
Keyword(s):  
Hasse Principle

Thue equations that simultaneously fail the Hasse principle

2021 ◽  
pp. 1-10
Author(s):  
PALOMA BENGOECHEA
Keyword(s):  
Positive Integer ◽  
Hasse Principle ◽  
Fixed Degree ◽  
Binary Forms ◽  
Absolute Value ◽  
Positive Proportion ◽  
The Absolute

Abstract We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.

On the Hasse principle for cubic surfaces

Mathematika ◽  
1966 ◽  
Vol 13 (2) ◽  
pp. 111-120 ◽  
Author(s):  
J. W. S. Cassels ◽  
M. J. T. Guy
Keyword(s):  
Hasse Principle ◽  
Cubic Surfaces

The Hasse Principle

2020 ◽  
pp. 121-140
Author(s):  
Daniel Coray
Keyword(s):  
Hasse Principle

scholarly journals Hasse principle for hermitian spaces over semi-global fields

2016 ◽  
Vol 458 ◽  
pp. 171-196
Author(s):  
Zhengyao Wu
Keyword(s):  
Hasse Principle ◽  
Global Fields

COUNTEREXAMPLES TO THE HASSE PRINCIPLE IN FAMILIES

2021 ◽  
pp. 1-10
Author(s):  
NGUYEN XUAN THO
Keyword(s):  
Hasse Principle ◽  
Quartic Surfaces

Abstract We generalise two quartic surfaces studied by Swinnerton-Dyer to give two infinite families of diagonal quartic surfaces which violate the Hasse principle. Standard calculations of Brauer–Manin obstructions are exhibited.

scholarly journals A positive proportion of Thue equations fail the integral Hasse principle

2019 ◽  
Vol 141 (2) ◽  
pp. 283-307 ◽  
Author(s):  
Shabnam Akhtari ◽  
Manjul Bhargava
Keyword(s):  
Hasse Principle ◽  
Positive Proportion
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