Advances on superelliptic curves and their applications / edited by Lubjana Beshaj, Tony Shaska, and Eustrat Zhupa.

"Proceedings of the NATO Advanced Study Institute on Hyperelliptic Curve Cryptography, Ohrid, Former Yugoslav Republic of Macedonia, 25 August-5 September, 2014"--Title page verso.

Includes bibliographical references at chapter ends, and indexes.

The case for superelliptic curves / L. Beshaj, T. Shaska, and E. Zhupa -- Weierstrass points of superelliptic curves / C. Shor and T. Shaska -- Theta functions of superelliptic curves / Lubjana Beshaj, Artur Elezi, and Tony Shaska -- Cyclic curves over the reals / M. Izquierdo and T. Shaska -- Reduction theory of binary forms / Lubjana Beshaj -- Sato-Tate groups of genus 2 curves / Kiran S. Kedlaya -- Heights on algebraic curves / T. Shaska and L. Beshaj -- Descent and covering collections / Michael Stoll -- Chabauty and the Mordell-Weil sieve / Samir Siksek -- Rational points on Jacobians of hyperelliptic curves / Jan Steffen Müller -- Explicit [italic]p-adic methods for elliptic and hyperelliptic curves / Jennifer S. Balakrishnan -- Error correcting quantum codes and algebraic curves / Artur Elezi -- Graph based cubical multivariate maps and their cryptographical applications / Michał Klisowski and Vasyl Ustimenko -- Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes / Artur Elezi and Tony Shaska -- Galois geometries, codes, and new invariants for incidence structures / Vladimir D. Tonchev.

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.

Online resource; title from PDF title page (EBSCO, viewed July 22, 2015).

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