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I'm interested as to what would constitute prerequisite reading for André Weil's book Basic Number Theory. For simplicity (and generality), you can assume that the reader can read anything that requires only the knowledge of undergraduate algebra, analysis, and elementary number theory. Thanks!

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While it is true that Weil appears to require that his reader appreciate Haar measure, I think there is serious risk of over-interpreting this. If anything, an attentive reading of the initial parts of Weil show exactly what one needs of invariant measures and integrals... and it is just the same as needed for Iwasawa-Tate's rewriting of Hecke's treatment of L-functions of number fields.

Rather, I think one might be happiest with a prior reading of a serious (as opposed to easy-intro) book on Alg No Th, such as Serge Lang's. After reading that more-conventional treatment, one will have an idea what Weil is accomplishing by seeming (!) to emphasize measure... as his foundation.

Although Weil's book contains a number of things difficult to find elsewhere, it is also rather quirky, and in a fashion not excessively reader-friendly. Having it be the second more-advanced book one has read on the subject is desirable.

(Systematic reading of whole books about functional analysis or measure-and-integration is surely not necessary, although, yes, of course, such background would provide a "complete-logical" background. It wouldn't explain the number theoretic motivation. And I note that the usual books on "real analysis" seem inordinately devoted to scaring us and making us worry about the legitimacy of doing anything at all... rather than enabling us to do more than we could previously.)

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"And I note that the usual books on "real analysis" seem inordinately devoted to scaring us and making us worry about the legitimacy of doing anything at all... rather than enabling us to do more than we could previously." Wow, I think there's no better way of putting it. –  Adrián Barquero Sep 1 '12 at 1:45
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:) Too bad, though. Powerful inertia of curriculum, unfortunately. Mandatory reliving of 100+ year old worries/traumas. Indeed, the late 19th-century viewpoint on "analysis" asked for more than it needed, in many ways, and it seemed to need Cantor's set theory, etc. Lebesgue, Beppo Levi, Frobenius, Hilbert, and many others showed that things turn out ok nevertheless. It disparages no one to not relive all that fretting. –  paul garrett Sep 1 '12 at 1:52
    
Thanks for this insightful answer. :) –  user5501 Sep 2 '12 at 16:40
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You need basic knowledge of harmonic analysis on locally compact abelian groups.

For example, I think Folland's book: A course in abstract harmonic analysis is more than enough for this.

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Thanks Makoto; what knowledge is required to read Folland's book? –  user5501 Sep 1 '12 at 0:23
    
I ask this because its table of contents and its series ("Studies in Advanced Mathematics") seem a bit intimidating. –  user5501 Sep 1 '12 at 0:43
    
@LovrePešut For examples, Folland's Real analysis and Rudin's Functional analysis. Folland said so in the preface of his book. –  Makoto Kato Sep 1 '12 at 0:46
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