Number theory

This book stems from lectures that were delivered at the three-week Advanced Instructional School on Ergodic Theory and Dynamical Systems held at the Indian Institute of Technology Delhi, from 4-23 December 2017, with the support of the National Centre for Mathematics, National Board for Higher Mathematics, Department of Atomic Energy, Government of India.

This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work.

This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view.

This book discusses special properties of integer sequences from a unique point of view.

This book offers a unique account on the life and works of Srinivasa Ramanujan-often hailed as the greatest "e;natural"e; mathematical genius.

This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar-including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India.

The book discusses major topics in complex analysis with applications to number theory.

The First Edition of the book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians in history whose life and works have things in common with Ramanujan.

This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications.

This book gathers original research papers and survey articles presented at the "e;International Conference on Class Groups of Number Fields and Related Topics,"e; held at Harish-Chandra Research Institute, Allahabad, India, on September 4-7, 2017.

This book offers an essential textbook on complex analysis.

This volume presents a collection of results related to the BSD conjecture, based on the first two India-China conferences on this topic.

In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory.

This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations.

This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes.

P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field.

The book intends to give a modern presentation of the classical Markov and Lagrange spectrum, which are fundamental objects from the theory of Diophantine approximations and of their several generalizations related to Dynamical Systems and Differential Geometry.

This is a book about Mathematics but not a book of Mathematics.

Natural numbers are the oldest human invention.

For a long time, all thought there was only one geometry - Euclidean geometry.

Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science.

Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science.

There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's.

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science.

This self-contained book is an exposition of the fundamental ideas of model theory.

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography.

This is the second in a series of three volumes dealing with important topics in algebra.

This is the first in a series of three volumes dealing with important topics in algebra.

This book introduces the reader to the fascinating world of modular forms through a problem-solving approach.

This exposition is primarily a survey of the elementary yet subtle innovations of several mathematicians between 1929 and 1934 that led to partial and then complete solutions to Hilbert's Seventh Problem (from the International Congress of Mathematicians in Paris, 1900).

EI presente texto es uno de los productos de un proyecto de investigación aprobado por Colciencias y la Universidad del Valle, realizado entre enero de 2005 y abril de 2008 bajo el título de "La constitución histórica de los números reales en la perspectiva de la formación de docente".

Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis.

The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions.

The subject of this book is probabilistic number theory.

Computers have stretched the limits of what is possible in mathematics.

The SCAN conference, the International Symposium on Scientific Com- puting, Computer Arithmetic and Validated Numerics, takes place bian- nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation).

This book grew out of our lectures given in the Oberseminar on 'Cod- ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001.

This monograph is intended to be a complete treatment of the metrical the- ory of the (regular) continued fraction expansion and related representations of real numbers.

This monograph on quantum wires and quantum devices is a companion vol- ume to the author's Quantum Chaos and Mesoscopic Systems (Kluwer, Dordrecht, 1997).

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2.

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics.

4.

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993.

Numbers .

The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications.

Approach your problems from the right end It isn't that they can't see the solution.

Finslerian Laplacians have arisen from the demands of modelling the modern world.

This book contains 33 papers from among the 41 papers presented at the Eighth International Conference on Fibonacci Numbers and Their Applications which was held at the Rochester Institute of Technology, Rochester, New York, from June 22 to June 26, 1998.