Advances on Superelliptic Curves and Their Applications
1st Edition
Published on 15. July 2015
388 pages
978-1-61499-520-3 (ISBN)
Description
This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves.
Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed.
The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.
Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed.
The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.
More details
Series
Language
English
Place of publication
London
Netherlands
Publishing group
IOS Press
Target group
Professional and scholarly
File size
3,24 MB
ISBN-13
978-1-61499-520-3 (9781614995203)
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Schweitzer Classification
Other editions
Additional editions
Lubjana Beshaj | Eustrat Zhupa
Advances on Superelliptic Curves and Their Applications
Book
07/2015
1st Edition
IOS Press,US
€171.12
Shipment within 10-15 days
Content
- Advances on Superelliptic Curves and Their Applications
- Preface
- Contents
- The case for superelliptic curves
- Weierstrass points of superelliptic curves
- Theta functions of superelliptic curves
- Cyclic curves over the reals
- Reduction theory of binary forms
- Sato-Tate groups of genus 2 curves
- Heights on algebraic curves
- Descent and Covering Collections
- Chabauty and theMordell-Weil Sieve
- Rational points on Jacobians of hyperelliptic curves
- Explicit p-adic methods for elliptic and hyperelliptic curves
- Error Correcting Quantum Codes and Algebraic Curves
- Graph based cubical multivariate maps and their cryptographical applications
- Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes
- Galois geometries, codes, and new invariants for incidence structures
- Subject Index
- Author Index
