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Algebraic geometry --- Hecke operators. --- Forms, Modular. --- Multiplication, Complex. --- 51 --- Hecke operators --- Forms, Modular --- Multiplication, Complex --- Complex multiplication --- Geometry, Algebraic --- Modular forms --- Forms (Mathematics) --- Operators, Hecke --- Operator theory --- Mathematics --- 51 Mathematics

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"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is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly.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.

Algebraic number theory --- Algebraïsche getallentheorie --- Nombres algébriques [Théorie des ] --- Algebraic number theory. --- 511.6 --- Number theory --- Algebraic number fields --- 511.6 Algebraic number fields --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra

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Revisits successive periods in the reception of the Disquisitiones as it studies which parts were taken up and when, which themes were further explored. This work also focuses on how specific mathematicians reacted to Gauss' book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others.

Number theory. --- Gauss, Carl Friedrich, --- Number study --- Numbers, Theory of --- Algebra --- Algebra. --- Number Theory. --- History of Mathematical Sciences. --- Mathematics --- Mathematical analysis --- Mathematics. --- History. --- Annals --- Auxiliary sciences of history --- Math --- Science

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In 1998, the editors convinced themselves that it was the right time to take stock of recent research concerning the modern history of number theory, and to evaluate in its light our comprehension of the development of this discipline as a whole. One issue at stake was to bring together historiographical results coming from different disciplines and linguistic domains which, we felt, had remained too often unaware of each other. We organized two meetings at theMathematisches Forschungsinstitut Oberw- fach: ?rstasmallRIP-workshopheldJune14-19,1999,amonghistoriansofnumber theoryandhistoriansofrelatedtopics, andthenalargerconferencewhichtookplace June 17-23, 2001, two hundred years after the publication of Carl Friedrich Gauss's DisquisitionesArithmeticae. Thelatterbroughttogetherhistoriansandphilosophers of mathematics with number theorists interested in the recent history of their ?eld. Two further meetings, organized by one of us in Vienna and Zürich the following years, continued our venture. Two concrete projects arose from these activities. One concerned the creation of resources, for scholars and students: we initiated a bibliography of secondary 1 literature on the History of Number Theory since 1800.

Number theory --- Algebra --- Mathematics --- algebra --- geschiedenis --- wiskunde --- getallenleer