Weil, Andre

Number Theory
An approach through history from Hammurapi to Legendre

Series: Modern Birkhauser Classics
Originally published as a monograph
1st ed. 1984. 4th printing, 2007, XXII, 376 p., 18 illus., Softcover
ISBN-10: 0-8176-4565-9
ISBN-13: 978-0-8176-4565-6

About this book

Number Theory or arithmetic, as some prefer to call it, is the oldest, purest, liveliest, most elementary yet sophisticated field of mathematics. It is no coincidence that the fundamental science of numbers has come to be known as the "Queen of Mathematics." Indeed some of the most complex conventions of the mathematical mind have evolved from the study of basic problems of number theory.

Andre Weil, one of the outstanding contributors to number theory, has written an historical exposition of this subject; his study examines texts that span roughly thirty-six centuries of arithmetical work ? from an Old Babylonian tablet, datable to the time of Hammurapi to Legendrefs Essai sur la Theorie des Nombres (1798). Motivated by a desire to present the substance of his field to the educated reader, Weil employs an historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. In the course of his study Weil accompanies the reader into the workshops of four major authors of modern number theory (Fermat, Euler, Lagrange and Legendre) and there he conducts a detailed and critical examination of their work. Enriched by a broad coverage of intellectual history, Number Theory represents a major contribution to the understanding of our cultural heritage

Table of contents

Preface.- Table of illustrations.- Abbreviations, basic references and notations.- Protohistory.- Fermat and his Correspondents.- Euler.- An Age of Transition: Lagrange and Legendre.- Additional bibliography and references.- Index nominum.- Index rerum.


Holzapfel, Rolf-Peter; Uludag, Muhammed; Yoshida, Masaaki (Eds.)

Arithmetic and Geometry Around Hypergeometric Functions
Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005

Series: Progress in Mathematics , Vol. 260
2007, Approx. 445 p., Hardcover
ISBN-10: 3-7643-8283-X
ISBN-13: 978-3-7643-8283-4

About this book

This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul during June 13-25, 2005. A wide range of topics related to hypergeometric functions is covered, thus giving a broad perspective of the state of the art in the field.

Written for:

Graduates, postgraduates and researchers

Keywords:

K3 surface
hyperbolic geometry
hypergeometric function
moduli space

Table of contents

Preface.- Contributions by D. Allcock, F. Beukers, J.A. Carlson, I.V. Dolgachev, A. Dzambic, R.-P. Holzapfel, A.N. Kochubei, S. Kondo, E. Looijenga, K. Matsumoto, T. Riedel, H. Shiga, J. Stienstra, D. Toledo, A.M. Uludag, J. Wolfart, M. Yoshida.- Problem Session.

Janas, J.; Kurasov, P.; Laptev, A.; Naboko, S.; Stolz, G. (Eds.)

Operator Theory, Analysis and Mathematical Physics

Series: Operator Theory: Advances and Applications , Vol. 174
2007, Approx. 270 p., Hardcover
ISBN-10: 3-7643-8134-5
ISBN-13: 978-3-7643-8134-9

About this book

This volume contains lectures delivered by the participants of the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics. The main topics are functional models of non-selfadjoint operators, spectral properties of Dirac and Jacobi matrices, Dirichlet-to-Neumann techniques, Lyapunov exponents methods, and inverse spectral problems for quantum graphs.

Table of contents

Introduction.- Contributions by P.A. Cohujari, M. Combescure, P. Exner, R.L. Frank, T. Ichinose, A.V. Kiselev, S. Kondej, J. Michor, A.B. Mikhailova, M. Nowaczyk, B.S. Pavlov, V.I. Ryzhii, V. Ryzhof, H. Schulz-Baldes, R.G. Shterenberg, L.O. Silva, S. Simonov, G. Teschl, A. Tikhonov.

*

Forster, K.-H.; Jonas, P.; Langer, H.; Trunk, C. (Eds.)

Operator Theory in Inner Product Spaces

Series: Operator Theory: Advances and Applications , Vol. 175
2007, Approx. 255 p., Hardcover
ISBN-10: 3-7643-8269-4
ISBN-13: 978-3-7643-8269-8

About this book

This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, which was held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation and extension theory of linear operators and relations in inner product spaces, including spectral analysis of differential operators, the theory of generalized Nevanlinna functions and related classes of functions, spectral theory of matrix polynomials, and problems from scattering theory.

Table of contents

Preface.- Contributions by T.Ya. Azizov, J. Behrndt, V. Derkach, A. Fleige, K.-H. Forster, S. Hassi, P. Jonas, M. Kaltenback, I. Karabash, A. Kostenko, H. Langer, A. Luger, C. Mehl, B. Nagy, H. Neidhardt, V. Pivovarchik, J. Rehberg, L. Rodman, A. Sandovici, L.I. Soukhotcheva, H. de Snoo, C. Trunk, H. Winkler, H. Woracek


Capogna, L., Danielli, D., Pauls, S.D., Tyson, J.T.

An Introduction to the Heisenberg Group
and the Sub-Riemannian Isoperimetric Problem

Series: Progress in Mathematics , Vol. 259
2007, Approx. 230 p., Hardcover
ISBN-10: 3-7643-8132-9
ISBN-13: 978-3-7643-8132-5

About this book

This book gives an up-to-date account of progress on Pansu's celebrated 1982 problem on the sub-Riemannian isoperimetric profile of the Heisenberg group, while simultaneously serving as an introduction to the general field of sub-Riemannian geometric analysis in this restricted context. The focus is on developing the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem and other questions in the sub-Riemannian calculus of variations.

Written for:

Graduate students and researchers in Analysis, Geometry, and Mathematical Physics

Keywords:

Cauchy-Riemann manifold
Sobolev space
contact geometry
evolution equations
geometric measure theory
immersions
minimal surface
quasiconformal mapping
sub-Riemannian geometry

Table of contents

Preface.- 1. The Isoperimetric Problem.- 2. The Heisenberg Group.- 3. Horizontal Geometry of Submanifolds.- 4. Geometric Measure Theory.- 5. The Isoperimetric Inequality.- 6. The Isoperimetric Profile of the Heisenberg Group.- 7. Sharp Constants for Other Geometric Inequalities.- Bibliography.- Index.

@