Maxima of Randomized Riemann Zeta Functions

Arguin, Belius, and Harper showed that the maximum of a random model of zeta function is $\exp(\log\log T−{3\over4}\log\log\log T+o(\log\log\log T))$ on the critical axis $\lbrack0,1/2+iT\rbrack$ as $T\rightarrow\infty$. Their proof uses an approximate tree structure hidden in the random model so as to use the results already well-known for branching random walk. We will show the construction of the random model of the Riemann zeta function, and describe the analogy with branching random walk, and how this analogy can be used to obtain the asymptotic of the maximum of randomized zeta function.

Warren Tai