Number theory

This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.

This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career.

In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest.

The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media).

This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.

The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan.

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda's 60th birthday.

Figurate numbers have a rich history with many applications.

This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms.

The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users.

This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates.

The binomial transform is a discrete transformation of one sequence into another with many interesting applications in combinatorics and analysis.

This volume is the result of the author's many-years of research in this field.

This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families, and on the canonical and subcanonical extensions of automorphic bundles.

This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations.

This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables.

This book is an introduction to the theory and application of modes - structures that capture the common underlying algebra of convex sets, affine spaces and certain ordered sets.

The material in this book is organized in such a way that the reader gets to significant applications quickly, and the emphasis is on the geometric understanding and use of new concepts.

This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics.

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used.

This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities.

This book covers selected topics in geometry, algebra, calculus and probability theory.

Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers.

Novel and important applications of number theory to graph theory and vice versa had been made in the past decade.

Number Mosaics has little in common with most other books of recreational mathematics.

The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory.

This book explains clearly and in detail the basic concepts and methods of calculations of the elementary theory of numbers.

In these lecture notes the student learns basic theorems of the subject (due to Sylow, Burnside, Schur and Frobenius).

Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications.

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980.

Spinors are used extensively in physics.

Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics.

This textbook presents the foundations of tensor calculus and the elements of tensor analysis.

Number theory is an important research field of mathematics.

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic 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.