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Number Theory
Paperback
Series: Classics in Mathematics
ISBN13: 9783540427490
Publisher: Springer
Published: Jan 10 2002
Pages: 640
Weight: 2.22
Height: 1.44 Width: 6.82 Depth: 8.72
Language: English
...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.
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