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.)
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.