scholarly journals Integral Hasse Principle and Strong Approximation for Markoff Surfaces

2020 ◽  
Author(s):  
Daniel Loughran ◽  
Vladimir Mitankin
Keyword(s):  
Strong Approximation ◽  
Hasse Principle

Abstract We study the failure of the integral Hasse principle and strong approximation for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer–Manin obstruction.

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.

A strong approximation for some non-stationary complex Gaussian processes

1981 ◽  
Vol 18 (2) ◽  
pp. 390-402 ◽  
Author(s):  
Peter Breuer
Keyword(s):  
Rate Of Convergence ◽  
Gaussian Processes ◽  
Strong Approximation ◽  
Approximation Theorem ◽  
Explicit Rate ◽  
Complex Valued ◽  
Strong Approximation Theorem

A strong approximation theorem is proved for some non-stationary complex-valued Gaussian processes and an explicit rate of convergence is achieved. The result answers a problem raised by S. Csörgő.

Strong approximation for ρ-mixing sequences

2012 ◽  
Vol 55 (10) ◽  
pp. 2159-2182
Author(s):  
ZhengYan Lin ◽  
YueXu Zhao
Keyword(s):  
Strong Approximation ◽  
Mixing Sequences

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
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