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#### The Quadratic Reciprocity Law

Springer International Publishing 2015; US$ 65.16This 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 classique

De Gruyter 2013; US$ 182.00Die Reihe widmet sich grundlegenden Texten der Wissenschaft und Philosophie der Antike und der islamischen Welt, die arabisch überliefert sind. Durch Bereitstellung kritischer Textausgaben und monographischer Untersuchungen werden der Forschung diejenigen Themenbereiche zugänglich gemacht, in denen sich die Wissenschaft zwischen der Antike... more...

#### Elliptic Diophantine Equations

De Gruyter 2013; US$ 140.00This book presents in a unified and concrete 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 the literature. Some results are hidden behind a number of routines in software... more...

#### Arithmetic Compactifications of PEL-Type Shimura Varieties

Princeton University Press 2013; US$ 175.00 US$ 159.25By 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 London 2012; US$ 46.69This 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 Curves

Princeton University Press 2012; US$ 87.50 US$ 79.63This 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 Paths

Springer London 2011; US$ 130.32This 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)

Princeton University Press 2010; US$ 60.00 US$ 54.60This 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 Varieties

Birkhäuser Basel 2009; US$ 65.16This 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 Dynamics

De Gruyter 2009; US$ 162.87The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question.... more...