Number theory

Helmut Hasse, H.G. Zimmer3540082751, 9783540082750

“…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 seomething 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 theoy locally, that is, at the completion of a valuation. Then ask for a miracle: that global validity is equivalent to local validity. … It is trite but true: Every number theorist should have this book on his or her shelf.” – IRVING KAPLANSKY IN BULETIN _OF THE AMERICAN MATH SOCIETY