scholarly journals Counting Rational Points on Algebraic Varieties

2006 ◽  
pp. 51-95 ◽  
Author(s):  
D. R. Heath-Brown
Keyword(s):  
Rational Points ◽  
Algebraic Varieties ◽  
Counting Rational Points

scholarly journals Counting rational points on algebraic varieties

2006 ◽  
Vol 132 (3) ◽  
pp. 545-578 ◽  
Author(s):  
T. D. Browning ◽  
D. R. Heath-Brown ◽  
P. Salberger
Keyword(s):  
Rational Points ◽  
Algebraic Varieties ◽  
Counting Rational Points

scholarly journals Counting rational points on quartic del Pezzo surfaces with a rational conic

2018 ◽  
Vol 373 (3-4) ◽  
pp. 977-1016
Author(s):  
T. D. Browning ◽  
E. Sofos
Keyword(s):  
Rational Points ◽  
Del Pezzo Surfaces ◽  
Del Pezzo ◽  
Counting Rational Points

scholarly journals Counting Rational Points of an Algebraic Variety over Finite Fields

2019 ◽  
Vol 74 (1) ◽  
Author(s):  
Shuangnian Hu ◽  
Xiaoer Qin ◽  
Junyong Zhao
Keyword(s):  
Finite Fields ◽  
Algebraic Variety ◽  
Rational Points ◽  
Counting Rational Points

scholarly journals Counting rational points on cubic curves

2010 ◽  
Vol 53 (9) ◽  
pp. 2259-2268 ◽  
Author(s):  
Roger Heath-Brown ◽  
Damiano Testa
Keyword(s):  
Rational Points ◽  
Cubic Curves ◽  
Counting Rational Points

scholarly journals Counting in hyperbolic spikes: The diophantine analysis of multihomogeneous diagonal equations

2018 ◽  
Vol 2018 (737) ◽  
pp. 255-300
Author(s):  
Valentin Blomer ◽  
Jörg Brüdern
Keyword(s):  
Circle Method ◽  
Rational Points ◽  
Arithmetic Functions ◽  
New Method ◽  
Algebraic Varieties ◽  
Asymptotic Formulae ◽  
Versatile Tool

AbstractA method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a versatile tool to count rational points on algebraic varieties defined by multi-homogeneous diagonal equations.

scholarly journals Counting Rational Points on Cubic Hypersurfaces

Mathematika ◽  
2007 ◽  
Vol 54 (1-2) ◽  
pp. 93-112 ◽  
Author(s):  
T. D. Browning
Keyword(s):  
Rational Points ◽  
Counting Rational Points ◽  
Cubic Hypersurfaces

scholarly journals Counting rational points on smooth cyclic covers

2012 ◽  
Vol 132 (8) ◽  
pp. 1741-1757 ◽  
Author(s):  
D.R. Heath-Brown ◽  
Lillian B. Pierce
Keyword(s):  
Rational Points ◽  
Cyclic Covers ◽  
Counting Rational Points
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