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Diophantine analysis

  • Histoire de l'analyse diophantienne classiqueby Roshdi Rashed

    De Gruyter 2013; US$ 154.00

    This is the first study of the history of Diophantine analysis and the theory of numbers from Ab? K?mil to Fermat (9th-17th century). It thus offers an elaborate and detailed overview on a fundamental chapter on classical mathematical thought and its relation to algebra and Diophantus? Arithmetica. more...

  • Elliptic Diophantine Equationsby Nikos Tzanakis

    De Gruyter 2013; US$ 126.00

    This book presents in a unified way the beautiful and deep mathematics, both theoretical and computational, on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in literature. Some results are even hidden behind a number of routines in software packages, like Magma.... more...

  • Arithmetic Compactifications of PEL-Type Shimura Varietiesby Kai-Wen Lan

    Princeton University Press 2013; US$ 150.00

    By 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 Groupsby Peter Schneider

    Springer 2012; US$ 69.95

    Representation 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 Curvesby Xinyi Yuan; Shou-wu Zhang; Wei Zhang

    Princeton University Press 2012; US$ 75.00

    This 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... more...

  • Euclidean Shortest Pathsby Fajie Li; Reinhard Klette

    Springer 2011; US$ 129.00

    This 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)by Sophie Morel

    Princeton University Press 2010; US$ 52.50

    This 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 Dynamicsby Andrei Khrennikov; Vladimir Anashin

    De Gruyter 2009; US$ 182.00

    This 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 Varietiesby T.D. Browning

    Springer 2009; US$ 89.99

    Describes 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 Numbersby Chung-Chun Yang; Pei-Chu Hu

    De Gruyter 2008; US$ 224.00

    The 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...