PI - Number Theory 1

Mathematics of Networks: Modulus Theory and Convex Optimization explores the question: “What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete ……続きを見る

Die digitale Revolution hat das 20. Jahrhundert geprägt - doch der nächste große Schritt steht bereits bevor: der Quantencomputer. Diese bahnbrechende Technologie verspricht, die Rechenleistung auf ……続きを見る

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addr……続きを見る

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developme……続きを見る

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general questio……続きを見る

The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses te……続きを見る

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extension……続きを見る

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as pr……続きを見る

This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory ……続きを見る

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 prerequ……続きを見る

Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomo……続きを見る

If we actually received messages from the stars, what would we do with them? Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Who is the Number King?……続きを見る

Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on ……続きを見る

Das Buch bietet eine neue Stoffzusammenstellung, die elementare Themen aus der Algebra und der Zahlentheorie verknüpft und für die Verwendung in Bachelorstudiengängen und modularisierten Lehramtsstu……続きを見る

If we actually received messages from the stars, what would we do with them? Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Who is the Number King?……続きを見る

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories;……続きを見る

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics w……続きを見る

This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, were first introduced i……続きを見る

The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy’s continuity theorem. This monograph focuses on this characteristic f……続きを見る

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as……続きを見る

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subj……続きを見る

The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. Th……続きを見る

This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed ……続きを見る