The Erdos-Kac theorem: an introduction to probabilistic number theory

by Dr V. Vinay Kumaraswamy (TIFR, Mumbai)

Friday 4 Jun 2021, 17:00 → 18:00 Asia/Kolkata

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Abstract: A famous result of Hardy and Ramanujan states that almost every large integer $N$ has approximately $\log \log N$ prime factors. This result was subsequently refined by Erdos and Kac, who proved that the distribution of the number of prime factors of an integer, when suitably normalised, may be modelled by the Gaussian random variable. In this talk, I will discuss some motivations of the Erdos-Kac theorem and outline its proof.