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Arithmetic Compactifications of PEL-Type Shimura Varieties
Princeton University Press 2013; US$ 150.00By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian... more...
Modular Representation Theory of Finite Groups
Springer 2012; US$ 54.99Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is... more...
The Gross-Zagier Formula on Shimura Curves
Princeton University Press 2012; US$ 150.00This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of... more...
Euclidean Shortest Paths
Springer 2011; US$ 99.99This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical... more...
On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)
Princeton University Press 2010; US$ 87.50This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of... more...
Applied Algebraic Dynamics
De Gruyter 2009; US$ 168.00This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative... more...
Quantitative Arithmetic of Projective Varieties
Springer 2009; US$ 99.00Describes counting rational points of bounded height on projective algebraic varieties. This book discusses the topic that lies at the interface of analytic number theory and Diophantine geometry. more...
Distribution Theory of Algebraic Numbers
De Gruyter 2008; US$ 196.00The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions ? Algebraic... more...
Diophantine Approximation
Springer 2008; US$ 139.99This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation. This includes contributions to Wolfgang Schmidt's subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine... more...
The Large Sieve and its Applications
Cambridge University Press 2008; US$ 90.00Explains new applications of the 'large sieve', an important tool of analytic number theory, presenting potential uses beyond this area. more...
