论文标题
Riemann-Siegel theta功能的精制渐近学
Refined asymptotics of the Riemann-Siegel theta function
论文作者
论文摘要
riemann-siegel theta函数$ \ vartheta（t）$以$ t \ to+\ infty $检查。使用$ \ log \，\ g（z）$的精制渐近扩展，表明$ \ vartheta（t）$的扩展包含一个越来越多的亚较高指数项的无限顺序，每个序列都乘以涉及$πt$的逆权力的渐近级数。给出了数值示例，以检测并确认这些指数的前三个存在。
The Riemann-Siegel theta function $\vartheta(t)$ is examined for $t\to+\infty$. Use of the refined asymptotic expansion for $\log\,\g(z)$ shows that the expansion of $\vartheta(t)$ contains an infinite sequence of increasingly subdominant exponential terms, each multiplied by an asymptotic series involving inverse powers of $πt$. Numerical examples are given to detect and confirm the presence of the first three of these exponentials.
