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Basic Number Theory

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This book is in the MAA's basic library list.

MAA Review

This is definitely a classic, but it is hardly “Basic.” The very first section includes a proof that there are no finite skew-fields, and the second famously begins by defining the p-adic absolute values in terms of the additive Haar measure on a locally compact topological field.

That out of the way, Weil’s classic exposition of local and global class field theory should certainly be on every young number theorist’s reading list.

BLL* — The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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