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From the Preface by K. Chandrasekharan: "The publication of this
collection of papers is intended as a service to the mathematical
community, as well as a tribute to the genius of CARL LUDWIG
SIEGEL... In the wide range of his interests, in his capacity to
uncover, to attack, and to subdue problems of great significance
and difficulty, in his invention of new concepts and ideas, in his
technical prowess, and in the consummate artistry of his
presentation, SIEGEL resembles the classical figures of
mathematics. In his combination of arithmetical, analytical,
algebraical, and geometrical methods of investigation, and in his
unerring instinct for the conceptual and structural, as distinct
from the merely technical, aspects of any concrete problem, he
represents the best type of modern mathematical thought. At once
classical and modern, his work has profoundly influenced the
mathematical culture of our time... this publication...will no
doubt stimulate generations of scholars to come." Volume IV
collects Siegels papers from 1968 to 1975.
From the Preface by K. Chandrasekharan: "The publication of this
collection of papers is intended as a service to the mathematical
community, as well as a tribute to the genius of CARL LUDWIG
SIEGEL. In the wide range of his interests, in his capacity to
uncover, to attack, and to subdue problems of great significance
and difficulty, in his invention of new concepts and ideas, in his
technical prowess, and in the consummate artistry of his
presentation, SIEGEL resembles the classical figures of
mathematics. In his combination of arithmetical, analytical,
algebraical, and geometrical methods of investigation, and in his
unerring instinct for the conceptual and structural, as distinct
from the merely technical, aspects of any concrete problem, he
represents the best type of modern mathematical thought. At once
classical and modern, his work has profoundly influenced the
mathematical culture of our time...this publication...will no doubt
stimulate generations of scholars to come." Volume III collects
Siegel's papers from 1945 to 1964.
From the Preface by K. Chandrasekharan: "The publication of this
collection of papers is intended as a service to the mathematical
community, as well as a tribute to the genius of CARL LUDWIG
SIEGEL, who is rising seventy. In the wide range of his interests,
in his capacity to uncover, to attack, and to subdue problems of
great significance and difficulty, in his invention of new concepts
and ideas, in his technical prowess, and in the consummate artistry
of his presentation, SIEGEL resembles the classical figures of
mathematics. In his combination of arithmetical, analytical,
algebraical, and geometrical methods of investigation, and in his
unerring instinct for the conceptual and structural, as distinct
from the merely technical, aspects of any concrete problem, he
represents the best type of modern mathematical thought. At once
classical and modern, his work has profoundly influenced the
mathematical culture of our time...this publication...will no doubt
stimulate generations of scholars to come." Volume II includes
Siegel's papers written between 1937 and 1944.
Carl Ludwig Siegel gave a course of lectures on the Geometry of
Numbers at New York University during the academic year 1945-46,
when there were hardly any books on the subject other than
Minkowski's original one. This volume stems from Siegel's
requirements of accuracy in detail, both in the text and in the
illustrations, but involving no changes in the structure and style
of the lectures as originally delivered. This book is an enticing
introduction to Minkowski's great work. It also reveals the
workings of a remarkable mind, such as Siegel's with its precision
and power and aesthetic charm. It is of interest to the aspiring as
well as the established mathematician, with its unique blend of
arithmetic, algebra, geometry, and analysis, and its easy
readability.
Carl Ludwig Siegel gave a course of lectures on the Geometry of
Numbers at New York University during the academic year 1945-46,
when there were hardly any books on the subject other than
Minkowski's original one. This volume stems from Siegel's
requirements of accuracy in detail, both in the text and in the
illustrations, but involving no changes in the structure and style
of the lectures as originally delivered. This book is an enticing
introduction to Minkowski's great work. It also reveals the
workings of a remarkable mind, such as Siegel's with its precision
and power and aesthetic charm. It is of interest to the aspiring as
well as the established mathematician, with its unique blend of
arithmetic, algebra, geometry, and analysis, and its easy
readability.
The description for this book, Transcendental Numbers. (AM-16),
will be forthcoming.
From the Preface (K. Chandrasekharan, 1966): "The publication of
this collection of papers is intended as a service to the
mathematical community, as well as a tribute to the genius of CARL
LUDWIG SIEGEL, who is rising seventy.In the wide range of his
interests, in his capacity to uncover, to attack, and to subdue
problems of great significance and difficulty, in his invention of
new concepts and ideas, in his technical prowess, and in the
consummate artistry of his presentation, SIEGEL resembles the
classical figures of mathematics. In his combination of
arithmetical, analytical, algebraical, and geometrical methods of
investigation, and in his unerring instinct for the conceptual and
structural, as distinct from the merely technical, aspects of any
concrete problem, he represents the best type of modern
mathematical thought. At once classical and modern, his work has
profoundly influenced the mathematical culture of our time."Volume
I includes Siegel's papers written between 1921 and 1937.
Uber die im folgenden behandelten Fragen der Himmelsmechanik habe
ich in Frankfurt am Main und Baltimore sowie wiederholt in
Gottingen und Princeton gelesen, am ausftihrlichsten in einem vier-
sttindigen Gottinger Kolleg des Wintersemesters 1951/52. Herr Dr.
J. MOSER, jetzt in ew York, hat damals eine sorgfaltige Xachschrift
angefertigt, welche dieser Veroffentlichung zugrunde liegt. Ich bin
kein Astronom yon Fach und habe deshalb auch keinen Versuch
gemacht, die tiblichen Methoden zur praktischen Bahnbestim- mung
erneut darzustellen, tiber die es bekanntlich gute Lehrbticher
gibt. Es wird sich yielmehr yorwiegend darum handeln, einige Ideen
und Resultate zu entwickeln, welche im Laufe der letzten 70 Jahre
tiber das Verhalten der Losungen von Differentialgleichungen im
groBen ent- standen sind, wobei allerdings die Anwendungen auf
HAMILToNsche Systeme und insbesondere die Bewegungsgleichungen des
Dreikorper- problems einen wichtigen Platz einnehmen. Auch hier
habe ich keine Vollstandigkeit angestrebt, sondern die Auswahl so
getroffen, wie sie durch personliches Interesse und die Hoffnung
auf Anregung der Horer im Rahmen einer Vorlesung geboten wurde.
Nach einleitenden Betrachtungen zur Transformationstheorie der
Differentialgleichungen ist das Ziel des ersten Kapitels eine
Darstellung der wichtigen Ergebnisse von K. F. SUNDMAN zum
Dreikorperproblem. Obwohl die SUNDMANschen Satze bald 50 Jahre alt
sind, so sind sie nur in klein em Kreise bekannt geworden und haben
auf die spatere Entwicklung kaum gewirkt. Nachst POINCARES
Leistungen zur Theorie der Differentialgleichungen gehoren SUNDMANs
Arbeiten trotz ihres speziellen Charakters vielleicht zu den
bedeutendsten neueren Ergeb- nissen auf dies em Gebiet.
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