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math.NT2023
Omega theorems for logarithmic derivatives of zeta and -functions
Daodao Yang
We establish several new -theorems for logarithmic derivatives of the Riemann zeta function and Dirichlet -functions. In particular, this improves on earlier work of Landau (…
math.NT2023
Mean values of ratios of the Riemann zeta function
Daodao Yang
It is proved that $$\int_{T}^{2T} \left|\frac{ζ\left(\frac{1}{2}+{\rm i} t\right)}{ζ\left(1+2{\rm i} t\right)}\right|^2 {\rm d} t = \frac{1}{ζ(2)} T \log T + \left( \frac{\log \fra…
math.NT2023
Extreme values of Dirichlet polynomials with multiplicative coefficients
Max Wenqiang Xu, Daodao Yang
We study extreme values of Dirichlet polynomials with multiplicative coefficients, namely \[D_N(t) : = D_{f,\, N}(t)= \frac{1}{\sqrt{N}} \sum_{n\leqslant N} f(n) n^{it}, \] where $…