Algebraic Number Theory: v. 322 (Grundlehren der mathematischen Wissenschaften)

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9783540653998: Algebraic Number Theory: v. 322 (Grundlehren der mathematischen Wissenschaften)
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This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.

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Críticas:

hful and unabridged reprint of the original edition of J. Neukirch’s excellent textbook on modern algebraic number theory ... . this unique classic in algebraic number theory is certainly of the highest advantage for new generations of students, teachers, and researchers in German-speaking mathematical communities, and therefore more than welcome. ... it will remain as one of the valuables in the legacy of an outstanding researcher and teacher in algebraic number theory forever." (Werner Kleinert, Zentralblatt MATH, Vol. 1131 (9), 2008)

Contraportada:

"The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner... The author discusses the classical concepts from the viewpoint of Arakelov theory.... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples.... The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook.... The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in Z.blatt f. Math., 1992 "The author's enthusiasm for this topic is rarely as evident for the reader as in this book. - A good book, a beautiful book." F. Lorenz in Jber. DMV 1995 "The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. Not only must it be missing from the library of no number theorist, but it can simply be recommended to every mathematician who wants to get an idea of modern arithmetic." J. Schoissengeier in Montatshefte Mathematik 1994

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Jürgen Neukirch
Verlag: Springer Berlin Heidelberg Mai 1999 (1999)
ISBN 10: 3540653996 ISBN 13: 9783540653998
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Buchbeschreibung Springer Berlin Heidelberg Mai 1999, 1999. Buch. Zustand: Neu. Neuware - From the review: 'The present book has as its aim to resolve a discrepancy in the textbook literature and . to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. . Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner. The author discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class field theory is . particularly rich in illustrating complements, hints for further study, and concrete examples. The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook. The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.' W. Kleinert in: Zentralblatt für Mathematik, 1992 596 pp. Englisch. Artikel-Nr. 9783540653998

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