Download or read book Die Analytische Zahlentheorie Classic Reprint written by Paul Bachmann and published by Forgotten Books. This book was released on 2017-10-14 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Die Analytische Zahlentheorie Vorlesungen hat der Verfasser nichts weiter jener Nachschrift entnommen, als einige unwesentlichere Punkte: die Begrundung der Formel (42) auf Seite 32, die Formulirung des Satzes in Nr. 4 des 3. Abschnittes, ferner, von ihrer Herleitung ab gesehen, die Integralformel (60) auf Seite 174, sowie die Ent wicklung auf Seite 335, welche zur Formel (51) das. Fuhrt. Gegenuber den Vorlesungen, welche vorzuglich den Stempel Krone cker'scher Forschung tragen, war es die Absicht des Verfassers bei der Ausarbeitung seines Werkes, getreu dem in der Vorrede zu den Elementen der Zahlentheorie ent wickelten Plane, von der analytischen Zahlentheorie in so engem Anschlusse, als es eine innerlich zusammenhangende Darstellung des Ganzen nur gestattet, an die Arbeiten der verschiedensten Forscher, welche sie ausgebildet, ein lebens volles Bild zu entwerfen, das nicht nur von ihrem Wesen, ihren Aufgaben, Methoden und Ergebnissen, sondern insbe sondere auch von ihrer Entwicklung eine deutliche Ansicht wie Einsicht gewahrt. Das Werk beschrankt sich aber hierbei auf Fragen der reellen Zahlentheorie, welche die hauptsachlichsten zahlentheo retischen Funktionen oder die Theorie der binaren quadra tischen Formen betreffen, weil die entsprechenden Fragen der hoheren Gebiete, soweit ihre Erorterung erforderlich ist oder noch ein wesentliches Interesse darbietet, erst bei der Dar stellung dieser letztern die geeignete Stelle finden. Es schliesst auch alle Anwendungen der Theorie der elliptischen Funktionen auf Zahlentheorie, denen ein besonderes Werk gewidmet wer den soll, vollstandig aus. Neben den Anwendungen der Ana lysis auf arithmetische Fragen, welche Dirichlet gelehrt hat, steht eine andere Verknupfung der Zahlentheorie mit analy tischen Gesichtspunkten, die man Hermite verdankt; sie charakterisirt sich weniger als eine Anwendung der Analysis auf hohere Arithmetik, als vielmehr als eine Einfuhrung des Stetigen selbst in die letztere, und konnte vielleicht nicht uneben als zahlentheoretische Analysis benannt werden. Auch sie findet passender an einer andern Stelle unsers Unternehmens ihren Platz und ihre volle Wurdigung; in diesem Werke mussen wir ganzlich von ihr Abstand nehmen. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book An Introduction to Classical Complex Analysis written by and published by Academic Press. This book was released on 1980-07-15 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Classical Complex Analysis
Download or read book Classical Analysis in the Complex Plane written by Robert B. Burckel and published by Springer Nature. This book was released on 2021-10-11 with total page 1123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative text presents the classical theory of functions of a single complex variable in complete mathematical and historical detail. Requiring only minimal, undergraduate-level prerequisites, it covers the fundamental areas of the subject with depth, precision, and rigor. Standard and novel proofs are explored in unusual detail, and exercises – many with helpful hints – provide ample opportunities for practice and a deeper understanding of the material. In addition to the mathematical theory, the author also explores how key ideas in complex analysis have evolved over many centuries, allowing readers to acquire an extensive view of the subject’s development. Historical notes are incorporated throughout, and a bibliography containing more than 2,000 entries provides an exhaustive list of both important and overlooked works. Classical Analysis in the Complex Plane will be a definitive reference for both graduate students and experienced mathematicians alike, as well as an exemplary resource for anyone doing scholarly work in complex analysis. The author’s expansive knowledge of and passion for the material is evident on every page, as is his desire to impart a lasting appreciation for the subject. “I can honestly say that Robert Burckel’s book has profoundly influenced my view of the subject of complex analysis. It has given me a sense of the historical flow of ideas, and has acquainted me with byways and ancillary results that I never would have encountered in the ordinary course of my work. The care exercised in each of his proofs is a model of clarity in mathematical writing...Anyone in the field should have this book on [their bookshelves] as a resource and an inspiration.”- From the Foreword by Steven G. Krantz
Download or read book Multiplicative Number Theory I written by Hugh L. Montgomery and published by Cambridge University Press. This book was released on 2007 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Download or read book Basic Complex Analysis written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.
Download or read book Quadratic Irrationals written by Franz Halter-Koch and published by CRC Press. This book was released on 2013-06-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T
Download or read book A Course in Analytic Number Theory written by Marius Overholt and published by American Mathematical Soc.. This book was released on 2014-12-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Download or read book The American Mathematical Monthly written by and published by . This book was released on 1971 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Books in Series written by and published by . This book was released on 1985 with total page 1858 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1980- issued in three parts: Series, Authors, and Titles.
Download or read book Lattice Points written by Ekkehard Krätzel and published by Springer Science & Business Media. This book was released on 1989-03-31 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a special problem of number theory, that is the estimation of the number of lattice points in large closed domains of ordinary Euclidean spaces. Circle and sphere problems, Dirichlet's divisor problem, the distribution of powerful numbers, and finite Abelian groups are also investigated. The object of this book is to acquaint the reader with the fundamental results and methods, so that follow up with the original papers is possible.
Download or read book Books in Series in the United States written by and published by . This book was released on 1966 with total page 1046 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systematics written by Ward C. Wheeler and published by John Wiley & Sons. This book was released on 2012-06-14 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematics: A Course of Lectures is designed for use in an advanced undergraduate or introductory graduate level course in systematics and is meant to present core systematic concepts and literature. The book covers topics such as the history of systematic thinking and fundamental concepts in the field including species concepts, homology, and hypothesis testing. Analytical methods are covered in detail with chapters devoted to sequence alignment, optimality criteria, and methods such as distance, parsimony, maximum likelihood and Bayesian approaches. Trees and tree searching, consensus and super-tree methods, support measures, and other relevant topics are each covered in their own sections. The work is not a bleeding-edge statement or in-depth review of the entirety of systematics, but covers the basics as broadly as could be handled in a one semester course. Most chapters are designed to be a single 1.5 hour class, with those on parsimony, likelihood, posterior probability, and tree searching two classes (2 x 1.5 hours).
Download or read book Dictionary Catalog of the University Library 1919 1962 written by University of California, Los Angeles. Library and published by . This book was released on 1963 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Analysis written by Edmund Landau and published by . This book was released on 2021-02 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Natural numbers, zero, negative integers, rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book.
Download or read book Global Spencerism written by and published by BRILL. This book was released on 2015-10-27 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today the name most closely associated with evolutionary theory is Charles Darwin. Given Darwin’s immense reputation it is easy to forget that Herbert Spencer, in his time, was just as famous as Darwin. It turns out that Spencer’s evolutionary thought was not what necessarily appealed to many of his readers, since they had their own sense of his identity and importance. By focusing on Spencer the evolutionist, scholars have tended to concentrate their attention on a rather narrow view of him that has come out of Anglo-American appropriations of his thought. Spencer was one of the first international, public intellectuals whose views on psychology, religion, sociology, ethics, education, and biology captured the imagination of readers all over the world. The chapters will cover the communication and appropriation of Spencer’s ideas in Russia, the Middle East, China, Japan, Mexico, Argentina, Brazil, the United States, Italy, Scandinavia, and France. Contributors are: Li Bin, Juan Manuel Rodriguez Caso, Gowan Dawson, Heloisa Maria Bertol Domingues, Marwa Elshakry, Mark Francis, G. Clinton Godart, Michael Gordon, Paola Govoni, Rosaura Ruiz Gutiérrez, Hans Henrik Hjermitslev, Ricardo Noguera-Solano, Adriana Novoa, Greg Radick, Nathalie Richard, Ke Zunke.
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Download or read book Geometric and Analytic Number Theory written by Edmund Hlawka and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been included. The translator, Prof. Charles Thomas, has solved the difficult problem of the German text into English in an admirable way. He deserves transferring our 'Unreserved praise and special thailks. Finally, we would like to express our gratitude to Springer-Verlag, for their commitment to the publication of this English edition, and for the special care taken in its production. Vienna, March 1991 E. Hlawka J. SchoiBengeier R. Taschner Preface to the German Edition We have set ourselves two aims with the present book on number theory. On the one hand for a reader who has studied elementary number theory, and who has knowledge of analytic geometry, differential and integral calculus, together with the elements of complex variable theory, we wish to introduce basic results from the areas of the geometry of numbers, diophantine ap proximation, prime number theory, and the asymptotic calculation of number theoretic functions. However on the other hand for the student who has al ready studied analytic number theory, we also present results and principles of proof, which until now have barely if at all appeared in text books.
