论文信息 - Low Pseudomoments of Euler Products

Low Pseudomoments of Euler Products

In this paper, we determine the order of magnitude of the 2 q-th pseudomoment of powers of the Riemann zeta function $\zeta(s)^{\alpha}$ for $0 \lt q\le 1/2$ and $0 \lt \alpha \lt 1$, completing the results of Bondarenko, Heap and Seip, and Gerspach. Our results also apply to more general Euler products satisfying certain conditions.

Youness Lamzouri | Maxim Gerspach

[1] N. Snaith,et al. Random Matrix Theory and ζ(1/2+it) , 2000 .

[2] Low Pseudomoments of the Riemann Zeta Function and Its Powers , 2019, 1909.10224.

[3] Adam J. Harper. MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS , 2017, Forum of Mathematics, Pi.

[4] K. Seip,et al. An inequality of Hardy–Littlewood type for Dirichlet polynomials , 2014, 1405.6516.

[5] Hugh L. Montgomery,et al. Multiplicative Number Theory I: Classical Theory , 2006 .

[6] M. Nair,et al. Short sums of certain arithmetic functions , 1998 .

[7] P. Shiu. A Brun-Titschmarsh theorem for multiplicative functions. , 1980 .

[8] Brian Conrey,et al. Pseudomoments of the Riemann zeta-function and pseudomagic squares , 2003, math/0307213.

[9] G. Tenenbaum,et al. On mean values of random multiplicative functions , 2012 .

[10] J. Zhao,et al. Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function , 2020, Journal of the London Mathematical Society.

[11] E. Saksman,et al. Integral means and boundary limits of Dirichlet series , 2007, 0712.0492.

[12] Almost sure large fluctuations of random multiplicative functions , 2020, 2012.15809.

[13] Pseudomoments of the Riemann zeta function , 2017, Bulletin of the London Mathematical Society.