# Low Pseudomoments of the Riemann Zeta Function and Its Powers

@article{Gerspach2019LowPO,
title={Low Pseudomoments of the Riemann Zeta Function and Its Powers},
author={Maxim Gerspach},
journal={arXiv: Number Theory},
year={2019}
}
The $2 q$-th pseudomoment $\Psi_{2q,\alpha}(x)$ of the $\alpha$-th power of the Riemann zeta function is defined to be the $2 q$-th moment of the partial sum up to $x$ of $\zeta^\alpha$ on the critical line. Using probabilistic methods of Harper, we prove upper and lower bounds for these pseudomoments when $q \le \frac{1}{2}$ and $\alpha \ge 1$. Combined with results of Bondarenko, Heap and Seip, these bounds determine the size of all pseudomoments with $q > 0$ and $\alpha \ge 1$ up to powers… Expand
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