SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.

This book analyzes the response of the Indonesian press to American foreign policy during the administrations of Presidents Bush and Obama. Situated in Southeast Asia, Indonesia is the world's fourth most populous country and the largest Muslim nation, and as such is a potentially vital economic and strategic partner to the US in the 21st century. Ever since Indonesian independence post World War II, relations to the US have been marked by ups and downs. The author argues that the way the Indonesian public perceives the world has an impact on the national self-image that again heavily influences national foreign affairs. For both the US and Indonesia, this is a crucial moment in bilateral relations. This study explores Indonesian media responses to American foreign policy by analyzing more than 400 press articles. In the context of President Obama's declared "pivot to Asia", both countries need to find a way to foster better relations.

Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer's work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. In the mid 1950's, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the rationals. Finally, in the late 1960's, Iwasawa [Iw 1 I] . made the fundamental discovery that there was a close connection between his work on towers of cyclotomic fields and these p-adic L-functions of Leopoldt-Kubota.

The small book by Shimura-Taniyama on the subject of complex multi is a classic. It gives the results obtained by them (and some by Weil) plication in the higher dimensional case, generalizing in a non-trivial way the method of Deuring for elliptic curves, by reduction mod p. Partly through the work of Shimura himself (cf. [Sh 1] [Sh 2], and [Sh 5]), and some others (Serre, Tate, Kubota, Ribet, Deligne etc.) it is possible today to make a more snappy and extensive presentation of the fundamental results than was possible in 1961. Several persons have found my lecture notes on this subject useful to them, and so I have decided to publish this short book to make them more widely available. Readers acquainted with the standard theory of abelian varieties, and who wish to get rapidly an idea of the fundamental facts of complex multi plication, are advised to look first at the two main theorems, Chapter 3, 6 and Chapter 4, 1, as well as the rest of Chapter 4. The applications of Chapter 6 could also be profitably read early. I am much indebted to N. Schappacher for a careful reading of the manu script resulting in a number of useful suggestions. S. LANG Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive Definite Involutions . . . 6 2. CM Types and Subfields. . . . . 8 3. Application to Abelian Manifolds. 4. Construction of Abelian Manifolds with CM 14 21 5. Reflex of a CM Type . . . . .

ARCHIVE COpy DO NOT REMOVE The public in industrialized countries shows a mounting concern about biological effects of electrical and magnetic fields. As a result, experimental studies on this subject are being published in increasing numbers throughout the world. Prof. H. L. Konig, of the Technical University of Munich, West Germany, a leading expert and pioneer in this field, has written an authoritative text in a lucid style which makes the material also accessible to lay readers. The book describes the effects of natural as well as artificial electromagnetic energies covering the en tire measurable frequency range from the highest frequencies, x-rays, through microwaves, radio waves, and finally extremely low frequency (ELF) waves. Cit ing the evidence from scientific studies in various countries, Konig also appraises the biologic effects of microwaves and high tension power lines, which have become controversial issues in recent years. Other contributions to the book have been made by Prof. Albert P. Krueger, University of California, Berkeley, on air ionization effects and by the mete orologist Walter Sonning on biometeorology, documenting the influence of atmo spheric electrical currents on health and disease. Moreover, the late Dr. Siegnot Lang, a former coworker of Dr. Konig, has contributed to this book."

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C j] in the function field of X(N) over C. Here j is the classical modular function. However, for arithmetic applications, one considers the curve as defined over the cyclotomic field Q(JlN) of N-th roots of unity, and one takes the integral closure either of Q j] or Z j], depending on how much arithmetic one wants to throw in. The units in these rings consist of those modular functions which have no zeros or poles in the upper half plane. The points of X(N) which lie at infinity, that is which do not correspond to points on the above affine set, are called the cusps, because of the way they look in a fundamental domain in the upper half plane. They generate a subgroup of the divisor class group, which turns out to be finite, and is called the cuspidal divisor class group."

It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.

A belian Varieties has been out of print for a while. Since it was written, the subject has made some great advances, and Mumford's book giving a scheme theoretic treatment has appeared (D. Mum- ford, Abelian Varieties, Tata Lecture Notes, Oxford University Press, London, 1970). However, some topics covered in my book were not covered in Mumford's; for instance, the construction of the Picard variety, the Albanese variety, some formulas concern- ing numerical questions, the reciprocity law for correspondences and its application to Kummer theory, Chow's theory for the K/k-trace and image, and others. Several people have told me they still found a number of sections of my book useful. There- fore I thank Springer-Verlag for the opportunity to keep the book in print. S. LANG v FOREWORD Pour des simplifications plus subs tan- tielles, Ie developpement futur de la geometrie algebrique ne saurait manquer sans do ute d' en faire apparaitre. It is with considerable pleasure that we have seen in recent years the simplifications expected by Weil realize themselves, and it has seemed timely to incorporate them into a new book. We treat exclusively abelian varieties, and do not pretend to write a treatise on algebraic groups. Hence we have summarized in a first chapter all the general results on algebraic groups that are used in the sequel. They are all foundational results.

The small book by Shimura-Taniyama on the subject of complex multi is a classic. It gives the results obtained by them (and some by Weil) plication in the higher dimensional case, generalizing in a non-trivial way the method of Deuring for elliptic curves, by reduction mod p. Partly through the work of Shimura himself (cf. [Sh 1] [Sh 2], and [Sh 5]), and some others (Serre, Tate, Kubota, Ribet, Deligne etc.) it is possible today to make a more snappy and extensive presentation of the fundamental results than was possible in 1961. Several persons have found my lecture notes on this subject useful to them, and so I have decided to publish this short book to make them more widely available. Readers acquainted with the standard theory of abelian varieties, and who wish to get rapidly an idea of the fundamental facts of complex multi plication, are advised to look first at the two main theorems, Chapter 3, 6 and Chapter 4, 1, as well as the rest of Chapter 4. The applications of Chapter 6 could also be profitably read early. I am much indebted to N. Schappacher for a careful reading of the manu script resulting in a number of useful suggestions. S. LANG Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive Definite Involutions . . . 6 2. CM Types and Subfields. . . . . 8 3. Application to Abelian Manifolds. 4. Construction of Abelian Manifolds with CM 14 21 5. Reflex of a CM Type . . . . .

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C j] in the function field of X(N) over C. Here j is the classical modular function. However, for arithmetic applications, one considers the curve as defined over the cyclotomic field Q(JlN) of N-th roots of unity, and one takes the integral closure either of Q j] or Z j], depending on how much arithmetic one wants to throw in. The units in these rings consist of those modular functions which have no zeros or poles in the upper half plane. The points of X(N) which lie at infinity, that is which do not correspond to points on the above affine set, are called the cusps, because of the way they look in a fundamental domain in the upper half plane. They generate a subgroup of the divisor class group, which turns out to be finite, and is called the cuspidal divisor class group."

It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.

The rich variety of Europe's history rolled into one thrilling account. This book takes you on a fascinating journey through the disasters, triumphs, people, power and politics that have shaped the Europe we know today - and you'll meet some incredible characters along the way! From Roman relics to Renaissance, World Wars and Eurovision, European History For Dummies packs in the facts alongside the fun and brings the past alive. * Accompanied by access to a value-add timeline and 'Who's Who in European History' section on dummies.com * This new edition contains an 8-page colour insert so you can see who, what, and where the ensuing historical action takes place.

This book is a riotous, irreverent account of the people and events that have shaped Britain. Always getting those kings and queens confused? Never sure what happened when? Then you need this book. Inside you'll find rip-roaring stories of power-mad kings, executions, invasions, high treason, global empire building, and forbidden love - not bad for a nation of stiff upper lips! * Revised and expanded to include the historical parliamentary elections of 2010 and the British mission in Afghanistan * Accompanied by access to a timeline and 'Who's Who in British History' section on dummies.com * This new edition contains an 8-page color insert so you can see who, what and where the ensuing historical action takes place

This book analyzes the response of the Indonesian press to American foreign policy during the administrations of Presidents Bush and Obama. Situated in Southeast Asia, Indonesia is the world's fourth most populous country and the largest Muslim nation, and as such is a potentially vital economic and strategic partner to the US in the 21st century. Ever since Indonesian independence post World War II, relations to the US have been marked by ups and downs. The author argues that the way the Indonesian public perceives the world has an impact on the national self-image that again heavily influences national foreign affairs. For both the US and Indonesia, this is a crucial moment in bilateral relations. This study explores Indonesian media responses to American foreign policy by analyzing more than 400 press articles. In the context of President Obama's declared "pivot to Asia", both countries need to find a way to foster better relations.

Die Auseinandersetzung im Umweltschutz tiber groBtechnische Risiken, z. B. bei der friedlichen Nutzung der Kernenergie oder neuerdings auch bei der Kohlenutzung (Saurer Regen) sind Ausdruck einer veranderten BewuBtseinslage in der GeselI- schaft. Die Technoiogie-Folgen mtissen starker beriicksichtigt werden. Technische GroBschaden und Umweltkatastrophen find en erhOhte Aufmerksamkeit in der Of- fentlichkeit. Sie werden als von Menschen verursachte Gefahren nicht mehr schick- salhaft wie Naturkatastrophen hingenommen. Verschiedene GroBtechnologien zeichnen sich zwar durch eine hoch entwickelte, qualifizierte Sicherheitstechnologie aus; das Gefahrdungspotential groBtechnischer Systeme hat he ute jedoch GroBen- ordnungen erreicht, daB Storfalle mit katastrophalen Konsequenzen flir Mensch und Umwelt trotz aller Sicherheitsvorkehrungen als entfernte Moglichkeiten prinzi- piell nicht ausgeschlossen werden konnen. Die technische Entwicklung hat uns in neue Dimensionen des Umgangs mit Energie, gefahrlichen Stoffen und anderen mit Gefahren verbundenen System en geflihrt. Lange Zeit wurde kaum wahrgenommen, daB die damit verbundene quantitative VergroBerung der Gefahren zu einer neuen QualiHit technischer Risiken geflihrt hat. Ich sehe daher in der Untersuchung von Risiko-und Sicherheitsfragen konventio- neller und neuer Technologien im Rahmen der F + E-Politik der Bundesregierung eine wichtige Aufgabe. Staatliche ForschungsfOrderung muB dazu beitragen, technologische Entwick- lungen in ihren Zusammenhangen und Auswirkungen zu erkennen, ihre Chancen und Risiken abzuwagen und Entscheidungen tiber die Nutzung von Technologien zu begriinden. Dieser Zieivorstellung dient der Forderschwerpunkt "Risiko-und Sicherheitsfor- schung" beim Bundesminister flir Forschung und Technologie. Forderungsziel ist die Minderung der groBtechnischen Gefahren und die rationale Analyse der ver- bleibenden Risiken. Der Schwerpunkt untersttitzt damit die unter der Zielrichtung "Technologiefolgenabschatzung" laufenden Arbeiten.

"Statistiken sind merkwurdige Dinge ...," dies wird so mancher Mediziner denken, wenn er sich mit der Biometrie befasst. Sei es im Rahmen seiner Ausbildung oder im Zuge wissenschaftlicher oder klinischer Studien, Kenntnisse der Statistik und Mathematik sind unentbehrlich fur die tagliche Arbeit des Mediziners. Ziel dieses Lehrbuches ist es, den Mediziner systematisch an biometrische Terminologie und Arbeitsmethoden heranzufuhren, um ihn schliesslich mit den Grundlagen der Wahrscheinlichkeitsrechung vertraut zu machen. Nach der Lekture dieses Buches halt der Leser ein Werkzeug in den Handen, das ihm bei der Losung medizinscher Fragestellungen hilft ebenso wie bei der Beschreibung von Ergebnissen wissenschaftlicher Studien und naturlich bei der Doktorarbeit "