Random Curves, Neal Koblitz

Автор: Joseph H. Silverman; John T. Tate
Название: Rational Points on Elliptic Curves
ISBN: 3319307576 ISBN-13(EAN): 9783319307572
Издательство: Springer
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Описание: Introduction.- Geometry and Arithmetic.- Points of Finite Order.- The Group of Rational Points.- Cubic Curves over Finite Fields.- Integer Points on Cubic Curves.- Complex Multiplication.

Автор: Haruzo Hida
Название: Elliptic Curves and Arithmetic Invariants
ISBN: 1489990925 ISBN-13(EAN): 9781489990921
Издательство: Springer
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Цена: 13275.00 р.
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Описание: This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.

Автор: Ash Avner, Gross Robert
Название: Elliptic Tales: Curves, Counting, and Number Theory
ISBN: 0691163502 ISBN-13(EAN): 9780691163505
Издательство: Wiley
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Описание: Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture

Автор: Robert S. Rumely
Название: Capacity Theory on Algebraic Curves
ISBN: 3540514104 ISBN-13(EAN): 9783540514107
Издательство: Springer
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Описание: Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. It brings out a connection between the classical Green`s functions of analysis and Neron`s local height pairings.

Автор: Christian Wei?
Название: Twisted Teichm?ller Curves
ISBN: 331904074X ISBN-13(EAN): 9783319040745
Издательство: Springer
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Описание: These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmuller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance.

Название: Introduction to Elliptic Curves and Modular Forms
ISBN: 1461269423 ISBN-13(EAN): 9781461269427
Издательство: Springer
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Цена: 7680.00 р.
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Описание: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory.

Автор: Hershel M. Farkas; Shaul Zemel
Название: Generalizations of Thomae`s Formula for Zn Curves
ISBN: 1461427584 ISBN-13(EAN): 9781461427582
Издательство: Springer
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Цена: 23058.00 р.
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Описание: This book provides a comprehensive overview of the theory of theta functions, and the necessary background for understanding and proving the Thomae formulae and their relationship to the Zn curves. The book is intended for graduate students in mathematics studying complex analysis, algebraic geometry, and number theory as well as mathematical physicists and physicists studying conformal field theory.

Автор: Haruzo Hida
Название: Elliptic Curves and Arithmetic Invariants
ISBN: 1461466563 ISBN-13(EAN): 9781461466567
Издательство: Springer
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Цена: 19564.00 р.
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Описание: This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.

Автор: John Cremona; Joan-Carles Lario; Jordi Quer; Kenne
Название: Modular Curves and Abelian Varieties
ISBN: 3034896212 ISBN-13(EAN): 9783034896214
Издательство: Springer
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Описание: It would be difficult to overestimate the influence and importance of modular forms, modular curves, and modular abelian varieties in the development of num- ber theory and arithmetic geometry during the last fifty years. These subjects lie at the heart of many past achievements and future challenges. For example, the theory of complex multiplication, the classification of rational torsion on el- liptic curves, the proof of Fermat's Last Theorem, and many results towards the Birch and Swinnerton-Dyer conjecture all make crucial use of modular forms and modular curves. A conference was held from July 15 to 18, 2002, at the Centre de Recerca Matematica (Bellaterra, Barcelona) under the title "Modular Curves and Abelian Varieties". Our conference presented some of the latest achievements in the theory to a diverse audience that included both specialists and young researchers. We emphasized especially the conjectural generalization of the Shimura-Taniyama conjecture to elliptic curves over number fields other than the field of rational numbers (elliptic Q-curves) and abelian varieties of dimension larger than one (abelian varieties of GL2-type).

Автор: Shrawan Kumar; M.S. Narasimhan; G?rard Laumon; Ulr
Название: Vector Bundles on Curves - New Directions
ISBN: 3540624015 ISBN-13(EAN): 9783540624011
Издательство: Springer
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Описание: The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. Drinfeld Shtukas (Lectures by G. Drinfeld modules and Elliptic Sheaves (Lectures by U.

Автор: Ernst-Ulrich Gekeler
Название: Drinfeld Modular Curves
ISBN: 3540172017 ISBN-13(EAN): 9783540172017
Издательство: Springer
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Автор: Jean-Daniel Boissonnat; Albert Cohen; Olivier Giba
Название: Curves and Surfaces
ISBN: 331922803X ISBN-13(EAN): 9783319228037
Издательство: Springer
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Описание: Preface.- Finite Element Approximation with Hierarchical B-Splines.- Non-linear Local Polynomial Regression Multiresolution Methods using ℓ1-norm Minimization with Application to Signal Processing.- A New Class of Interpolatory L-splines with Adjoint End Conditions.- On a New Conformal Functional for Simplicial Surfaces.- Evaluation of Smooth Spline Blending Surfaces using GPU.- Implicit Equations of Non-degenerate Rational Bezier Quadric Triangles.- Support Vector Machines for Classification of Geometric Primitives in Point Clouds.- Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration.- New Bounds on the Lebesgue Constants of Leja Sequences on the Unit Disc and on ℜ-Leja Sequences.- A Curvature Smooth Lofting Scheme for Singular Point Treatments.- A Consistent Statistical Framework for Current-Based Representations of Surfaces.- Isotropic M]obius geometry and i-M circles on singular isotropic Cyclides.- Symbolic Computation of Equi-affine Evolute for Plane B-spline Curves.- On-line CAD Reconstruction with Accumulated Means of Local Geometric Properties.- Analysis of Intrinsic Mode Functions Based on Curvature Motion-like PDEs.- Differential Geometry Revisited by Biquaternion Clifford Algebra.- Ridgelet Methods for Linear Transport Equations.- Basis Functions for Scattered Data Quasi-interpolation.- Optimality of a Gradient Bound for Polyhedral Wachspress Coordinates.- Mass Smoothers in Geometric Multigrid for Isogeometric Analysis.- On the Set of Trajectories of the Control Systems with Limited Control Resources.- High Order Reconstruction from Cross-sections.- Adaptive Atlas of Connectivity Maps.- Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation.- Combination of Piecewise-geodesic Curves for Interactive Image Segmentation.- A Fully-nested Interpolatory Quadrature Based on Fej er's Second Rule.- CINPACT-splines: A Class of C1 Curves with Compact Support.- Error Estimates for Approximate Operator Inversion via Kernel-based Methods.- Boundary Controlled Iterated Function Systems.- Construction of Smooth Isogeometric Function Spaces on Singularly Parameterized Domains.- Reflexive Symmetry Detection in Single Image.