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math.NT2013
On a hybrid fourth moment involving the Riemann zeta-function
Aleksandar Ivić, Wenguang Zhai
We provide explicit ranges for for which the asymptotic formula \begin{equation*} \int_0^T|ζ(1/2+it)|^4|ζ(σ+it)|^{2j}dt \;\sim\; T\sum_{k=0}^4a_{k,j}(σ)\log^k T \quad(j\in\math…
math.NT2013
Conditional Results for a Class of Arithmetic Functions: a variant of H. L. Montgomery and R. C. Vaughan's method
Xiaodong Cao, Wenguang Zhai
Let and be positive integers such that and . Define the arithmetic function by $$ \sum_{n=1}^{\infty}\fra…