Bøger af Serge Lang

Here are the collected papers of Serge Lang, who has made numerous contributions to mathematics. One of the top mathematicians of our time, Lang received the American Mathematical Society's Cole Prize, and the Prix Carriere from the French Academy of Sciences.

Serge Lang is one of the top mathematicians of our time. Part of a four-volume set, this resource collects key research papers written by Lang and highlight the innumerable contributions he made in diverse fields in mathematics.

The purpose of this text is to provide a self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, this one begins with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion.

For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.

For many years, Serge Lang has given talks on selected items in mathematics which could be extracted at a level understandable by those who have had calculus.

At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications.

Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures.

The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory;

Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field.

Covers various basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences.

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

Deals with modern algebra.

It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms."Lang's books are always of great value for the graduate student and the research mathematician.

This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra.

By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q.

A basic advanced text in its field, this monograph for undergraduates and graduate students in mathematics requires some background in elementary qualitative algebraic geometry and the elementary theory of algebraic groups. 1959 edition.

Covers the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. This title is suitable for those taking the first calculus course, in high school or college.

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas.

This book is meant as a text for a first-year graduate course in analysis. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.

Vielleicht waren Sie iiberrascht, wenn jemand behauptete, daB Ma­ thematik etwas ausgesprochen SchOnes sei. Doch sollten Sie wissen, daB es Leute gibt, die sich ihr ganzes Leben lang mit Mathematik befassen und dort genauso schopferisch tatig sind wie ein Komponist in der Mu­ sik. Gewohnlich ist der Mathematiker damit beschiiftigt, ein Problem zu lOsen, und aus diesem ergeben sich dann wieder neue, ebenso schone Probleme wie das gerade geloste. N atiirlich sind mathematische Pro­ bleme oft recht schwierig und - wie in anderen Wissenschaften auc- nur zu verstehen, wenn man das Gebiet griindlich studiert hat und es gut kennt. 1981 hat mich Jean Brette, der die Mathematikabteilung des Palais de la Decouverte (Naturwissenschaftliches Museum) in Paris leitet, ein­ geladen, dort eine Vorlesung abzuhalten, Oder besser gesagt, ein Ge­ sprach mit der Offentlichkeit zu flihren. Niemals zuvor hatte ich vor einem nichtmathematischen Publikum vorgetragen, und somit war dies eine Herausforderung: Wiirde es mir gelingen, einem solchen Samstag­ nachmittagsauditorium klarzumachen, was es bedeutet, Mathematik zu betreiben, warum man sich mit Mathematik befaBt? Vnter "Mathema­ tik" verstehe ich hier reine Mathematik. Das soIl jedoch nicht etwa he i­ Ben, daB reine Mathematik besser sei als andere Arten von Mathematik; aber ich und eine Reihe anderer betreiben nun mal reine Mathematik, und darum geht es im folgenden.

This is the third version of a book on differential manifolds. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations.

This text in basic mathematics is ideal for high school or college students. It provides a firm foundation in basic principles of mathematics and thereby acts as a springboard into calculus, linear algebra and other more advanced topics.

The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory.

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms.

While the first part is suitable for an introductory course at undergraduate level, the additional topics covered in the second part give the instructor of a gradute course a great deal of flexibility in structuring a more advanced course.