Algebraic curves mod 𝔭 and arithmetic groups

1966 ◽  
pp. 265-271 ◽  
Author(s):  
Yasutaka Ihara
Keyword(s):  
Algebraic Curves ◽  
Arithmetic Groups

Algebraic Curves over Finite Fields

1991 ◽  
Author(s):  
Carlos Moreno
Keyword(s):  
Finite Fields ◽  
Algebraic Curves ◽  
Curves Over Finite Fields

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Arithmetic groups and Salem numbers

1992 ◽  
Vol 75 (1) ◽  
pp. 97-102 ◽  
Author(s):  
B. Sury
Keyword(s):  
Arithmetic Groups ◽  
Salem Numbers

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

Invariant Algebraic Curves and Hyperelliptic Limit Cycles of Liénard Systems

2021 ◽  
Vol 20 (2) ◽  
Author(s):  
Xinjie Qian ◽  
Yang Shen ◽  
Jiazhong Yang
Keyword(s):  
Limit Cycles ◽  
Algebraic Curves ◽  
Liénard Systems ◽  
Invariant Algebraic Curves

scholarly journals Real plane algebraic curves with prescribed singularities

Topology ◽  
1993 ◽  
Vol 32 (4) ◽  
pp. 845-856 ◽  
Author(s):  
Eugenii Shustin
Keyword(s):  
Algebraic Curves ◽  
Real Plane

scholarly journals Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves

2012 ◽  
Vol 365 (7) ◽  
pp. 3373-3396 ◽  
Author(s):  
Jun Lu ◽  
Sheng-Li Tan
Keyword(s):  
Algebraic Curves ◽  
Singular Fiber ◽  
Chern Numbers

Algebraic Curves

Nature ◽  
1951 ◽  
Vol 167 (4259) ◽  
pp. 962-962
Author(s):  
H. T. H. PIAGGIO
Keyword(s):  
Algebraic Curves
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