scholarly journals Composition algebras over algebraic curves of genus zero

1993 ◽  
Vol 337 (1) ◽  
pp. 473-493 ◽  
Author(s):  
Holger P. Petersson
Keyword(s):  
Algebraic Curves ◽  
Genus Zero ◽  
Composition Algebras

scholarly journals Integer points on algebraic curves with exceptional units

1997 ◽  
Vol 63 (2) ◽  
pp. 145-164 ◽  
Author(s):  
Dimitrios Poulakis
Keyword(s):  
Elliptic Equations ◽  
Algebraic Curves ◽  
Irreducible Polynomial ◽  
Algebraic Number Field ◽  
Genus Zero ◽  
Integer Points ◽  
Regular Functions ◽  
Affine Curves ◽  
Absolutely Irreducible Polynomial ◽  
Integral Solutions

AbstractLet F(X, Y) be an absolutely irreducible polynomial with coefficients in an algebraic number field K. Denote by C the algebraic curve defined by the equation F(X, Y) = 0 and by K[C] the ring of regular functions on Cover K. Assume that there is a unit ϕ in K[C] − K such that 1 − ϕ is also a unit. Then we establish an explicit upper bound for the size of integral solutions of the equation F(X, Y) = 0, defined over K. Using this result we establish improved explicit upper bounds on the size of integral solutions to the equations defining non-singular affine curves of genus zero, with at least three points at ‘infinity’, the elliptic equations and a class of equations containing the Thue curves.

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.

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
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