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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)
Book purchase
Number theory, Helmut Hasse
- Language
- Released
- 2002
Payment methods
- Title
- Number theory
- Language
- English
- Authors
- Helmut Hasse
- Publisher
- Springer
- Released
- 2002
- ISBN10
- 354042749X
- ISBN13
- 9783540427490
- Series
- Classics in mathematics
- Category
- Mathematics
- Description
- 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)