were the notes for 3, 6, and 8 ever completed?

Warmly,

Ryan

*[Links updated -T.]*

How does the entropy decrement argument end up leading to a proof of the prime number theorem, roughly? Does it allow one to get around dealing with zero-free regions?

]]>The entropy decrement argument can be used to establish a number of cases of (the logarithmically averaged version of) Chowla’s conjecture, particularly when combined with the Matomaki-Radziwill theorem and the circle method; but there are some more recent applications of the method that do not require these additional tools (for instance, my student has recently used this method to obtain a new proof of the prime number theorem), so I have decided to give it a separate set of notes (particularly since the use of that method requires a review of the Shannon entropy inequalities, which are rather separate from the other techniques in this set of notes.

I will not cover Diophantine approximation or discrepancy in these notes (and indeed will be omitting several other core topics in analytic number theory, notably sieve theory). Montgomery’s “Ten lectures in harmonic analysis” is still quite a good general reference for this subject.

]]>2. Would Diophantine objects and discrepancy be covered?

]]>I wish I could audit this course!

Is there any chance you could record the lectures and make the course publicly available online?

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