| The Theory of Algebraic Number Fields 1998 Edition Contributor(s): Hilbert, David (Author), Lemmermeyer, F. (Introduction by), Adamson, I. T. (Translator) |
|
 |
ISBN: 3540627790 ISBN-13: 9783540627791 Publisher: Springer OUR PRICE: $132.99 Product Type: Hardcover - Other Formats Published: August 1998 Annotation: This book is a translation into English of Hilbert's "Theorie der algebraischen Zahlk?rper" best known as the "Zahlbericht," first published in 1897, in which he provided an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht provided also a firm foundation for further research in the subject. It is based on the work of the great number theorists of the nineteenth century. The Zahlbericht can be seen as the starting point of all twentieth century investigations in algebraic number theory, reciprocity laws and class field theory. For this English edition an Introduction has been added by F. Lemmermeyer and N. Schappacher. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | History & Philosophy |
| Dewey: 512.74 |
| LCCN: 98042185 |
| Physical Information: 1.05" H x 6.38" W x 9.53" (1.55 lbs) 351 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is- chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati- cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory. |