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OK. You must have thought more about this than I just did, but the separation "Algebraic -- analytic", also for the functions themselves, is a separation that I have never seen in the literature. For example, in what sense is
Riemann zeta more analytic than Dedekind? Maybe reorganize into something
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Well, the point of naming it "Algebraic conjectures" was as a contrast to the "Analytic conjectures", i.e. what an algebraic number theorist might study versus an analytic number theorist. Also, the
Langlands conjecture that is mentioned isn't about special values, it's about decomposing the zeta
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like: automorphic vs. non-automorphic (or whatever title is best for things like
Riemann, Dedekind, ..., motivic L-functions)?
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OK. I suggest renaming the caption "Algebraic conjectures" to something like "
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