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#### Quantitative Arithmetic of Projective Varieties

Springer 2009; US$ 89.99Describes 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...

#### Lectures on Arakelov Geometry

Cambridge University Press 1992; US$ 48.00An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory. more...

#### Modular Representation Theory of Finite Groups

Springer 2012; US$ 69.95Representation 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...

#### Galois Representations in Arithmetic Algebraic Geometry

Cambridge University Press 1998; US$ 104.00Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'. more...

#### Perfect, Amicable and Sociable Numbers

World Scientific Publishing Company 1996; US$ 134.00This book is about perfect, amicable and sociable numbers, with an emphasis on amicable numbers, from both a mathematical and particularly a computational point of view. Perfect and amicable numbers have been studied since antiquity, nevertheless, many problems still remain. The book introduces the basic concepts and results of perfect, amicable and... more...

#### Chinese Remainder Theorem

World Scientific Publishing Company 1996; US$ 92.00Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. It is a perfect combination of beauty and utility or, in the words of Horace, omne tulit punctum qui miscuit utile dulci. Known already for ages, CRT continues to present itself in new contexts and open vistas for new types of applications. So far, its usefulness has been obvious... more...

#### Diophantine Analysis

Taylor and Francis 2005; US$ 99.95While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine approximations... more...

#### Histoire de l'analyse diophantienne classique

De Gruyter 2013; US$ 154.00This 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...

#### 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...

#### The Gross-Zagier Formula on Shimura Curves

Princeton University Press 2012; US$ 75.00This 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... more...