# Oleksiy Klurman (University of Bristol) - On the random Chowla conjecture

Dates: | 14 June 2022 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Speaker: | Oleksiy Klurman |

Abstract : A celebrated conjecture of Chowla in analytic number theory asserts that for the Liouville function $\lambda(n)$ and any non-square polynomial $P(n)$ one expects cancellations $\sum_{n\le x}\lambda(n)=o(x)$ In the case $P(n)=n$ this corresponds to the prime number theorem, but the conjecture is widely open for any polynomial $P$ of $\deg P \ge 2.$ In 1944, Wintner proposed to study random model for this question where $\lambda(n)$ is replaced by a random multiplicative function The goal of the talk is to discuss recent advances in understanding the distribution and the size of the largest fluctuations of appropriately normalized partial sums $\sum_{n\le x}f(n)$ (mostly due to Harper) and my recent joint work with I. Shkredov and M. Xu aiming to understand $\sum_{n\le x}f(P(n))$ for any polynomial of $\deg P\ge 2.$

### Speaker

Oleksiy Klurman

Organisation: University of Bristol