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Seminar

Chowla's Conjecture for Random Multiplicative Functions

Speaker
Besfort Shala (University of Bristol)
Date
Wed, Oct 23 2024, 1:00pm
Location
383N
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Abstract: Let f be a Steinhaus or Rademacher random multiplicative function. Even though a lot is known about partial sums of f over positive integers due to work of Harper, the exact distribution is still elusive. However, partial sums of f over some restricted sets of positive integers are better understood and are expected/known to mimic a sum of independent random variables, in the sense that they satisfy a central limit theorem and/or law of iterated logarithm. There are several results in this direction such as summing over: (i) integers with a restricted number of prime factors (Hough, Harper), (ii) integers in a short interval (Chatterjee-Sound, Sound-Xu), (iii) values of integer polynomials in the Steinhaus case (Klurman-Shkredov-Xu). The latter may be viewed as a random analogue for Chowla's conjecture or the related Elliott's conjecture. In this talk, I will give a survey of the above results and discuss joint work with Jake Chinis, where we address the random analogue of Chowla's conjecture for Rademacher multiplicative functions. If time permits, I will also discuss some open questions in this area, some of which we address in ongoing joint work with Christopher Atherfold.