某些数论误差项的卷积和均方估计
Convolutions and mean square estimates of certain number-theoretic error terms
摘要：
当$f(x)$是一个合适的数论误差项时，我们研究了卷积函数$$ C[f(x)] := \int_1^x f(y)f({x\over y}) {{\rm d} y\over y} $$。$C[f(x)]$的渐近性和上界是从$f(x)$的均方界导出的。给出了一些应用，特别是对$|ζ(1/2+ix)|^{2k}$和解析数论中的经典Rankin-Selberg问题的应用.
英文摘要：
We study the convolution function $$ C[f(x)] := \int_1^x f(y)f({x\over y}) {{\rm d} y\over y} $$ when $f(x)$ is a suitable number-theoretic error term. Asymptotics and upper bounds for $C[f(x)]$ are derived from mean square bounds for $f(x)$. Some applications are given, in particular to $|ζ(1/2+ix)|^{2k}$ and the classical Rankin--Selberg problem from analytic number theory.
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。
