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#### Advances in the Theory of Numbers

Springer New York 2015; US$ 84.23The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory. The proof by Andrew Wiles (with Richard Taylor) of Fermat?s last theorem published in 1995 illustrates... more...

#### Value Distribution in p-adic Analysis

World Scientific Publishing Company 2015; US$ 152.00 US$ 124.64The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk... more...

#### Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)

Princeton University Press 2016; US$ 90.00 US$ 72.00The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations... more...

#### Abelian Varieties with Complex Multiplication and Modular Functions

Princeton University Press 2016; US$ 130.00 US$ 104.00Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such... more...

#### Are Numbers Real?

St. Martin's Press 2016; US$ 28.99Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers... more...

#### The Selberg-Arthur Trace Formula

Springer Berlin Heidelberg 2006; US$ 22.45This book based on lectures given by James Arthur discussesthe trace formula of Selberg and Arthur. The emphasis islaid on Arthur's trace formula for GL(r), with severalexamples in order to illustrate the basic concepts. The bookwill be useful and stimulating reading for graduate studentsin automorphic forms, analytic number theory,... more...

#### Singular Modular Forms and Theta Relations

Springer Berlin Heidelberg 2006; US$ 22.45This research monograph reports on recent work on the theoryof singular Siegel modular forms of arbitrary level.Singular modular forms are represented as linearcombinations of theta series. The reader is assumed toknowonly the basic theory of Siegel modular forms. more...

#### Mixed Motives and Algebraic K-Theory

Springer Berlin Heidelberg 2006; US$ 44.92The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations... more...

#### Directions in Infinite Graph Theory and Combinatorics

Elsevier Science 2016; US$ 72.95This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts... more...

#### A Collection of Contributions in Honour of Jack van Lint

Elsevier Science 2016; US$ 72.95This collection of contributions is offered to Jack van Lint on the occasion of his sixtieth birthday and appears simultaneously in the series Topics in Discrete Mathematics and as a special double volume of Discrete Mathematics (Volumes 106/107). It is hoped that the papers selected, all written by experts in their own fields, represent the many interesting... more...