Lemma 5.12 . [0549] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Lemma 5.12 .
Let Q ≤ 1 Q\leq 1 C n > 0 C_{n}>0
(5.152) C n − 1 ⋅ e y ⋅ ( − y ) β − α \displaystyle C_{n}^{-1}\cdot e^{y}\cdot(-y)^{\beta-\alpha} ≤ Ψ ♭ ( β , α , y ) ≤ e y ⋅ ( − y ) β − α , \displaystyle\leq\Tri(\fb,\fa,y)\leq e^{y}\cdot(-y)^{\beta-\alpha},
(5.153) C n − 1 ⋅ ( − y ) − β \displaystyle C_{n}^{-1}\cdot(-y)^{-\beta} ≤ Φ ♯ ( β , α , y ) ≤ C n ⋅ ( − y ) − β . \displaystyle\leq\Ku(\fb,\fa,y)\leq C_{n}\cdot(-y)^{-\beta}.
for all y ≤ − 1 y\leq-1