Number theory

著者

書誌事項

Number theory

Helmut Hasse ; English translation edited and prepared for publication by Horst Günter Zimmer

（Die Grundlehren der mathematischen Wissenschaften, Bd. 229）

Springer-Verlag, 1980

  • : gw
  • : us

タイトル別名

Zahlentheorie

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注記

Corrected and enl. translation of Zahlentheorie, 3rd ed.: Berlin : Akademie-Verlag, 1969

Includes bibliographical references and indexes

内容説明・目次

内容説明

From the reviews: ..".a fine book ... treats algebraic number theory from the valuation-theoretic viewpoint. When it appeared in 1949 it was a pioneer. Now there are plenty of competing accounts. But Hasse has something extra to offer. This is not surprising, for it was he who inaugurated the local-global principle (universally called the Hasse principle). This doctrine asserts that one should first study a problem in algebraic number theory locally, that is, at the completion of a vaulation. Then ask for a miracle: that global validity is equivalent to local validity. Hasse proved that miracles do happen in his five beautiful papers on quadratic forms of 1923-1924. ... The exposition is discursive. ... It is trite but true: Every number-theorist should have this book on his or her shelf." (Irving Kaplansky in Bulletin of the American Mathematical Society, 1981)

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