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Diophantine analysis

  • The Quadratic Reciprocity Lawby Oswald Baumgart; Franz Lemmermeyer

    Springer International Publishing 2015; US$ 89.99

    This book is the English translation of Baumgart?s thesis on the early proofs of the quadratic reciprocity law (?Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise?), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre,... more...

  • Histoire de l'analyse diophantienne classiqueby Roshdi Rashed

    De Gruyter 2013; US$ 168.00

    This is the first study of the history of Diophantine analysis and the theory of numbers from Ab? K?mil to Fermat (9 th -17 th 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$ 133.00

    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,... more...

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

    Princeton University Press 2013; US$ 165.00

    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 London 2012; US$ 69.95

    This book provides a concise introduction to modular representation theory for masters-level students. It details basic results, tools, and techniques as well as compares group theoretic and module theoretic concepts. more...

  • The Gross-Zagier Formula on Shimura Curvesby Xinyi Yuan; Shou-wu Zhang; Wei Zhang

    Princeton University Press 2012; US$ 82.50

    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 Li Fajie; Reinhard Klette

    Springer London 2011; US$ 159.00

    This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements. more...

  • On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)by Sophie Morel

    Princeton University Press 2010; US$ 58.00

    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...

  • Quantitative Arithmetic of Projective Varietiesby Timothy D. Browning

    Birkhäuser Basel 2009; US$ 89.99

    This book examines the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties. more...

  • Applied Algebraic Dynamicsby Vladimir Anashin; Andrei Khrennikov

    De Gruyter 2009; US$ 196.00

    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...