6 Ergebnisse.

Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series¿and infinite series in general¿are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turn...

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers.From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATH...

There is now a large body of theory concerning algebraic varieties over finite fields, and many conjectures exist in this area that are of great interest to researchers in number theory and algebraic geometry. This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields, with special focus on the Tate conjecture and the Lichtenbaum Milne formula for the central value of the L-function. It combines theoretical and num...

The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry ...