Ergodic properties of the Liouville function and applications

Abstract: The Liouville function is a multiplicative function that encodes important information related to distributional properties of the prime numbers. A conjecture of Chowla states that the values of the Liouville function fluctuate between plus and minus in such a random way, that all sign patterns of a given length appear with the same frequency. The Chowla conjecture remains largely open and in this talk we will see how ergodic theory combined with some feedback from number theory allows us to establish two variants of this conjecture. Key to our approach is an in-depth study of measure preserving systems that are naturally associated with the Liouville function. The talk is based on joint work with Bernard Host.

combinatoricsnumber theory

Audience: researchers in the topic

Webinar in Additive Combinatorics

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