Rachid Caich

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math.NT2024

Almost sure upper bound for a model problem for multiplicative chaos in number theory

Rachid Caich

The goal of this work is to prove a new sure upper bound in a setting that can be thought of as a simplified function field analogue. This result is comparable to a recent result o…

math.NT2024

Almost sure upper bound for random multiplicative functions

Rachid Caich

Let $ε > 0$ . Let $f$ be a Steinhaus or Rademacher random multiplicative function. We prove that we have almost surely, as $x \to + \infty$ , $$ \sum_{n \leqslant x} f(n) \ll…

math.NT2024

Random multiplicative functions and typical size of character in short intervals

Rachid Caich

We examine the conditions under which the sum of random multiplicative functions in short intervals, given by $\sum_{x < n ⩽ x + y} f (n)$ , exhibits the phenomenon of \textit{be…