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Drinfeld Modules
This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics ...
Topics in the Theory of Algebraic Function Fields
The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
Algebraic Curves and Finite Fields
Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.
Álgebra superior
El texto puede usarse en los cursos básicos de álgebra que se ofrecen en diversas universidades o institutos tecnológicos. A pesar de que el enfoque del libro es formal, este puede usarse para cursos con un enfoque menos formal. Los ejemplos resueltos a lo largo de todo el libro, llevan al lector de la mano a una mejor comprensión de los temas presentados. Al final de cada unidad se plantean ejercicios tanto de corte teórico como de corte práctico y están diseñados para que el lector logre un adecuado manejo de los contenidos del libro.
Mathematical Reviews
None
Recent Developments And Applications In Mathematics And Computer Science - Proceedings Of The College
This book contains some invited lectures on subjects as diverse as document preparation systems, fractals, number theory, graph colouring and neural networks.
Mayan Visions
A significant work by one of anthropology's most important scholars, this book provides an introduction to the Chiapas Mayan community of Mexico, better known for their role in the Zapatista Rebellion.
Das Schweizer Buch
None
Number Theory in Function Fields
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.
