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if if In INCREASING integral integral is is is is

large. left-hand left-hand LEMMA Lemma Lemma Lemma

make mapping

ζ=2-1e-π/2|η|0<ξ2<ξ1σe-π/2;ζlog((ζ-iη0)-1)

ΔRσξη0η. R. ξ*δ*, |ζ|ζ0. |η|/ξξ1, ξ20<ξ<ξ*|η0|<δζ=ξ+iη|η|<δ*.=ξ+iηΔζ=ξ+iηΔζ0, ζΔ, ζ0, ζΔ.

u(ζu(ξ)dcΘR(c)>0, Δ={ζ=ξ+iη||η|<2eπ/2ξ}. 0<σ<min(δ-|η0|, log(r01)),

D=D(η0, σ)={ζ|Reζ>0, |ζ-iη0|<σ}. |η|<δ0=min(2δ/3, 12log(r0-1)),

1πlog|η|ξ+O(1)-(log|η|ξ+O(1))*u(ξ)u(ξ)dcΘR(c)=1πlog|η|ξ+O(1)u(ζ)u(ξγdcΘR(c)+uξ)u(ξ)dcΘR(c)u(ξ1+iη0)u(ξ.+iη0)dcΘD(c)|1πlogξ1ξ2+π4u(ξ)u(ζ)dcΘR(c)(12+o(1))(log|η|ξ+O(1))*

need need

obtain of of of of of of On on other

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positive proof Proof

oatisfied satisfies second set side side SLOWLY small small Stolz Stolz such such sufficientlyoufficiently sufficiently sufficiently

Cake taking that that The The the the the the the then Theorem Theorem these this

UNBOUNDED

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