Course summary

Lecture	Topic	References
1	Introduction, convergence in distribution, two elementary results	[Kowalski, Ch 1]
2	Example of a non-generic limiting distribution arising from Euler's totient function	[Kowalski, Ch 1]
3	The moment problem	[Billingsley, Ch's 26, 30]
4	The method of moments	[Billingsley, Ch's 25, 30]
5	The Erdős-Kac Theorem Download The Erdős-Kac Theorem	[Kowalski, Ch 2]
Problem set
6	The Selberg Central Limit Theorem. Introduction. Short Dirichlet polynomials over primes with Gaussian limiting distribution.	[Kowalski, Ch 4], [Harper, §§12-13 ], [Radziwiłł - Soundararajan]
7	Proof strategy. Download Proof strategy. Proofs of some auxiliary results.	[Radziwiłł - Soundararajan], [Harper], [Kowalski, Ch 4]
8	Truncating the exponential series Proposition 3	[Radziwiłł - Soundararajan, Prop. 3] [Kowalski, Ch 4.4], [Harper, §14]
9	Comparing the short Dirichlet polynomial $LaTeX: M\left(s\right)$ $M\left(s\right)$ to $LaTeX: \zeta(s)$ $\zeta(s)$ [slides Download slides]	[Radziwiłł - Soundararajan, Prop. 4] [Kowalski, Ch 4.3]
10	[Continuation from last time.] Proof of Selberg's Lemma [slides: form p. 54 Download slides: form p. 54]	[Radziwiłł - Soundararajan, Lemma. 4]