Number theory

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001.

The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems.

the attention of The publication of Charles Pisot's thesis in 1938 brought to the mathematical community those marvelous numbers now known as the Pisot numbers (or the Pisot-Vijayaraghavan numbers).

Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography.

Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics.

This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999.

To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000.

This volume began as the last part of a one-term graduate course given at the Fields Institute for Research in the Mathematical Sciences in the Autumn of 1993.

The book introduces new techniques that imply rigorous lower bounds on the com- plexity of some number-theoretic and cryptographic problems.

On the 16th of October 1843, Sir William R.

What is order that is not based on simple repetition, that is, periodicity?

Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology.

This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona.

This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958.

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering.

To date, the theoretical development of q-calculus has rested on a non-uniform basis.

This book contains survey papers based on the lectures presented at the 3rd International Winter School "e;Modern Problems of Mathematics and Mechanics"e; held in January 2010 at the Belarusian State University, Minsk.

Tamari lattices originated from weakenings or reinterpretations of the familar associativity law.

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface.

Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane ?

This twelfth volume in the Poincare Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics.

The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.

This book started with Lattice Theory, First Concepts, in 1971.

In the last ?

This book develops a new theory in convex geometry, generalizing positive bases and related to Caratheordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization.

This expanded textbook, now in its second edition, is a practical yet in depth guide to cryptography and its principles and practices.

This book brings together the impact of Prof.

This volume presents the revised papers of the 14th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2020, which took place online during August 10-14, 2020.

This text is intended for a one-semester course in cryptography at the advanced undergraduate/Master's degree level.

This proceedings volume gathers selected, peer-reviewed papers presented at the 2nd International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2021, which was virtually held on July 1-2, 2021 by the University of Salamanca, Spain.

This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS).

This monograph describes and implements partially homomorphic encryption functions using a unified notation.

The Hardy-Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists.

This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets.

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brasov, Romania, from May 13th to 17th, 2019.

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume.

This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics.

This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications.

This volume presents the collection of mathematical articles by Martin Kneser, reprinted in the original language - mostly German -, including one yet unpublished.

Mahler measure, a height function for polynomials, is the central theme of this book.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.