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Modular Formsby Toshitsune Miyake
Springer 2006; US$ 129.00Provides the basic knowledge of elliptic modular forms necessary to understand the developments in number theory. This book includes general theory of modular groups, Hecke operators, the unit groups of quaternion algebras, and more. Eisenstein series with parameter are discussed following the work of Shimura: Eisenstein series. more...
Bilinear Integrable Systemsby Ludwig Faddeev; Pierre van Moerbeke; Franklin Lambert
Springer 2006; US$ 239.00Representation Theory and Automorphic Formsby Toshiyuki Kobayashi; Wilfried Schmid; Jae Hyun Yang
Springer 2007; US$ 89.95Intended for both graduate students and researchers, this volume features the invited papers, written by leading mathematicians in related fields, which track the progress in the fields of representation theory and automorphic forms, and their association with number theory and differential geometry. more...
Quantization and Arithmeticby Andre Unterberger
Springer 2008; US$ 59.95The primary aim of this book is to create situations in which the zeta function, or other L-functions, will appear in spectral-theoretic questions. A secondary aim is to connect pseudo-differential analysis, or quantization theory, to analytic number theory. Both are attained through the analysis of operators on functions on the line by means of their diagonal matrix elements against families of arithmetic coherent states: these are families of discretely supported measures on the line, transforming in specific ways under the part of the metaplectic representation or, more generally, representations from the discrete series of SL(2, R), lying above an arithmetic group such as SL(2, Z). more...
Binary Quadratic Formsby Johannes Buchmann; Ulrich Vollmer
Springer 2007; US$ 109.00The book deals with algorithmic problems related to binary quadratic forms, such as finding the representations of an integer by a form with integer coefficients, finding the minimum of a form with real coefficients and deciding equivalence of two forms. In order to solve those problems, the book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. The book explains applications to cryptography. It requires only basic mathematical knowledge. more...
Modular Forms on Schiermonnikoogby Bas Edixhoven; Gerard van der Geer; Ben Moonen
Cambridge University Press 2008; US$ 87.00A collection of articles presenting the state of the art in the topic of modular forms. more...
Quadrangular Algebras. (MN-46):by Richard M. Weiss
Princeton University Press 2005; US$ 52.50This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E 6 , E 7 , and E 8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space... more...
Quadratic form theory and differential equationsby John Gregory
Elsevier Science & Technology 1981; US$ 175.00In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression... more...
Quadratic Forms, Linear Algebraic Groups, and Cohomologyby Jean-Louis Colliot-Thelene; Skip Garibaldi; R. Sujatha; Venapally Suresh
Springer 2010; US$ 149.00The invited papers collected in this volume address topics related to the research of Raman Parimala (plenary speaker at the upcoming ICM 2010). These themes focus primarily on the interplay between algebra, number theory, and algebraic geometry. The included contributions cover exciting research in areas such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces. more...
Modular Forms and Functionsby Robert A. Rankin
Cambridge University Press 1977; US$ 65.00This book provides an introduction to the theory of elliptic modular functions and forms. more...









