scholarly journals Counting points of homogeneous varieties over finite fields

2010 ◽  
Vol 2010 (645) ◽  
Author(s):  
Michel Brion ◽  
Emmanuel Peyre
Keyword(s):  
Finite Fields ◽  
Homogeneous Varieties ◽  
Counting Points

scholarly journals Counting Points on Curves and Abelian Varieties Over Finite Fields

2001 ◽  
Vol 32 (3) ◽  
pp. 171-189 ◽  
Author(s):  
Leonard M. Adleman ◽  
Ming-Deh Huang
Keyword(s):  
Finite Fields ◽  
Abelian Varieties ◽  
Counting Points

scholarly journals Equivariant Poincaré Polynomials and Counting Points over Finite Fields

2002 ◽  
Vol 247 (2) ◽  
pp. 435-451 ◽  
Author(s):  
M. Kisin ◽  
G.I. Lehrer
Keyword(s):  
Finite Fields ◽  
Counting Points

Harmonic Analysis Related to Homogeneous Varieties in Three Dimensional Vector Spaces over Finite Fields

2012 ◽  
Vol 64 (5) ◽  
pp. 1036-1057 ◽  
Author(s):  
Doowon Koh ◽  
Chun-Yen Shen
Keyword(s):  
Finite Fields ◽  
Three Dimensional ◽  
Vector Spaces ◽  
Extension Problem ◽  
Dimensional Vector ◽  
Complete Mapping ◽  
Plane Passing ◽  
Size Condition ◽  
Distance Problem ◽  
Homogeneous Varieties

Abstract In this paper we study the extension problem, the averaging problem, and the generalized Erdős-Falconer distance problem associated with arbitrary homogeneous varieties in three dimensional vector spaces over finite fields. In the case when the varieties do not contain any plane passing through the origin, we obtain the best possible results on the aforementioned three problems. In particular, our result on the extension problem modestly generalizes the result by Mockenhaupt and Tao who studied the particular conical extension problem. In addition, investigating the Fourier decay on homogeneous varieties enables us to give complete mapping properties of averaging operators. Moreover, we improve the size condition on a set such that the cardinality of its distance set is nontrivial.

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