Number Theory category: 319 books
Weyl Group Multiple Dirichlet Series
Type A Combinatorial Theory (AM-175)
Language: English
Release Date: July 5, 2011
Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series...
Exploring the Riemann Zeta Function
190 years from Riemann's Birth
Language: English
Release Date: September 11, 2017
Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic...
Irregularities in the Distribution of Prime Numbers
From the Era of Helmut Maier's Matrix Method and Beyond
Language: English
Release Date: July 4, 2018
This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis...
Neverending Fractions
An Introduction to Continued Fractions
Language: English
Release Date: July 3, 2014
Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature...
by Peter M. Higgins
Language: English
Release Date: February 24, 2011
Language: English
Release Date: February 24, 2011
Numbers are integral to our everyday lives and feature in everything we do. In this Very Short Introduction Peter M. Higgins, the renowned mathematics writer, unravels the world of numbers; demonstrating its richness, and providing a comprehensive view of the idea of the number. Higgins paints a picture...
Reassessing Riemann's Paper
On the Number of Primes Less Than a Given Magnitude
Language: English
Release Date: May 26, 2018
In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular...
Probabilistic Diophantine Approximation
Randomness in Lattice Point Counting
Language: English
Release Date: October 6, 2014
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of...
Convolution and Equidistribution
Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)
Language: English
Release Date: January 24, 2012
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions...
by Mark Joshi
Language: English
Release Date: March 17, 2015
Language: English
Release Date: March 17, 2015
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such...
The Story of Algebraic Numbers in the First Half of the 20th Century
From Hilbert to Tate
Language: English
Release Date: January 18, 2019
The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results...
Algebra 2
Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier
Language: English
Release Date: May 3, 2017
This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1–5) does...
How Numbers Work
Discover the strange and beautiful world of mathematics
Language: English
Release Date: May 1, 2018
Discover the incredible connection between numbers and reality itself!
Think of a number between one and ten...
No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw...
by Konrad Knopp
Language: English
Release Date: April 26, 2013
Language: English
Release Date: April 26, 2013
This classic work, written in a clear and interesting style, with many exercises, offers a thorough and reliable treatment of an important branch of higher analysis. It lends itself well to use in course work; however, because of its consistent clear illustrations of theoretical difficulties, the...
The Number Mysteries
A Mathematical Odyssey through Everyday Life
Language: English
Release Date: May 24, 2011
Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generation's foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of numbers and how, despite...