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> What Lindelof says is that the size of the output is always bounded by ε% as many digits as the input, for ANY (arbitrarily miniscule) ε > 0. Is there are re
by ascar 5y ago
> What Lindelof says is that the size of the output is always bounded by ε% as many digits as the input, for ANY (arbitrarily miniscule) ε > 0.
Is there are reason or benefit of stating it like that rather than saying the fraction of output and input digit size asymptotically approaches zero? Or did I misunderstand the explanation?
- gavagai691 5y agoThinking about digit size is sort of fine for simplification / not turning off general audiences with equations, but a bit of a pain to think about if , e.g., the things you're comparing might be smaller than one. What Lindelof says more precisely is that for any ε > 0 and any L-function L(s), there is a constant C_(ε,L) (depending only on ε and L, but crucially not on s) such that |L(s)| <= C_ε (1+|Im(s)|)^ε.
- CrushItNerds519 5y agoThere may be some linguistic benefits to the "epsilon" formulation when discussing subconvexity rather than Lindelof. For instance, I think "the output is eventually bounded by 24% of the input" sounds more natural than "the limsup of output/input approaches something less than 24%".