Riemann-Siegel θ函数的精化渐近性
Refined asymptotics of the Riemann-Siegel theta function
摘要：
针对$t\to+\infty$检验Riemann-Siegel θ函数$\vartheta(t)$。$\log\,\g(z)$的精细渐近展开的使用表明，$\vartheta(t)$的展开包含一个无穷序列的越来越次显性的指数项，每个乘以一个渐近级数涉及$πt$的逆幂。数值例子给出检测和确认这些指数的前三个的存在。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
