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Number Theory

Author: Henri Cohen
Publisher: Springer Science & Business Media
ISBN: 0387499237
Size: 42.61 MB
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The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Algorithmic Number Theory

Author: Alf J. van der Poorten
Publisher: Springer Science & Business Media
ISBN: 3540794557
Size: 42.65 MB
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The ?rst Algorithmic Number Theory Symposium took place in May 1994 at Cornell University. The preface to its proceedings has the organizers expressing the hope that the meeting would be “the ?rst in a long series of international conferencesonthe algorithmic,computational, andcomplexity theoreticaspects of number theory.” ANTS VIII was held May 17–22, 2008 at the Ban? Centre in Ban?, Alberta, Canada. It was the eighth in this lengthening series. The conference included four invited talks, by Johannes Buchmann (TU ´ Darmstadt),AndrewGranville(Universit´edeMontr´ eal),Fran¸ coisMorain(Ecole Polytechnique),andHughWilliams(UniversityofCalgary),apostersession,and 28 contributed talks in appropriate areas of number theory. Each submitted paper was reviewed by at least two experts external to the Program Committee; the selection was made by the committee on the basis of thoserecommendations.TheSelfridgePrizeincomputationalnumbertheorywas awardedtotheauthorsofthebestcontributedpaperpresentedattheconference. The participants in the conference gratefully acknowledge the contribution made by the sponsors of the meeting. May 2008 Alf van der Poorten and Andreas Stein (Editors) Renate Scheidler (Organizing Committee Chair) Igor Shparlinski (Program Committee Chair) Conference Website The names of the winners of the Selfridge Prize, material supplementing the contributed papers, and errata for the proceedings, as well as the abstracts of the posters and the posters presented at ANTS VIII, can be found at: http://ants.math.ucalgary.ca.

Number Theory

Author: Kalman Gyoery
Publisher: Walter de Gruyter
ISBN: 3110809796
Size: 30.42 MB
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The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Algebraic Geometry And Number Theory

Author: Hussein Mourtada
Publisher: Birkhäuser
ISBN: 331947779X
Size: 40.63 MB
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This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Zur Algebraischen Geometrie

Author: Bartel L. van der Waerden
Publisher: Springer
ISBN: 9783642617836
Size: 58.65 MB
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Als ich 1945 in MUnster zu studieren begann, war van dec Waerdens "Mo­ deme Algebra" eines dec wenigen Bticher, die ich mir in diesen schwierigen Zeiten leihen konnte. Wie vielen Studenten so war also auch mir . ,dervan dec Waerden" vertraut von Anfang des Studiums an. lch lernte van dec Waerden einige Jahre spaler kennen, und er sagte miT, wie merkwiirdig es sei, daB alle Mathematiker ibn wegen dieses Buches kennen, das Vorlesungen von Emil Artin und Emmy Noether benutzt, wahrend seine wirklichen mathemati­ schen Leistungen gam woanders Uigen. In dem Gesprach zeigte sich dann, dall van dec Waerden seine Arheiten zur algebraischen Geometrie nnd insbe­ sondere die in den Mathematischen Annalen erschienene Reihe "Zur alge­ braischen Geometrie" 1 die es in weiteren Jahren his zur NT. 20 bringen sollte, fUr das Wichtigste hielt. (Etwa 30 Jahre spater war ich zu einem Essen zu Ehren der Trager des Ordens Pour Ie Merite fUr Wissenschaft und Kunste ein­ geladen. Die beiden Ordenstrager van der Waerden und Elias Canetti unter­ hielten sich. Canetti bedauerte, dall man ibn hauptsachlich wegen seines Bu­ ches ,. Die gerettete Zunge" kenne, wahrend andere Schriften doch viet wich­ tiger seien. Van der Waerden rief aus "Aber mir geht es doch gaOl genau so mit meinem Algebra-Buch". ) Van der Waerden ist ein so ungewohnlich vielseitiger Mathematiker mit bedeutenden Buchem und Arbeiten aus zahlreichen weit von einander ent· fernten Gebieten, dal3 die Entscheidung des Verlages, diese Setecta der alge­ braischen Geometrie zu widmen, sicberlich nicht selbstverstiindlich war.

Advanced Topics In Computational Number Theory

Author: Henri Cohen
Publisher: Springer Science & Business Media
ISBN: 1441984895
Size: 30.67 MB
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Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.

Lectures On The Theory Of Algebraic Numbers

Author: E. T. Hecke
Publisher: Springer Science & Business Media
ISBN: 9780387905952
Size: 44.39 MB
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. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.