Analytic Methods in Number Theory
For a copy of the course syllabus, click
here

Click here for some
homework problems. I will add to these later on.

Click
here for a recent article on the ErdosKac theorem.

Click
here for a recent article on the divisor function by Kevin Ford,
which has consequences for the Erdos multiplication table problem I
talked about in class (see page 7 of that article).
Click here for a short writeup
of the estimate for the number of positive integers in [1,x] that
are coprime to an integer q.
Click here for a short
writeup of the ``convolution method'' I mentioned in class.
Click here for some basic
facts about the Riemann Zeta function. On Thursday, Jan. 25 I will
hand out some xeroxed notes on the Prime Number Theorem and the
Riemann Zeta function  be patient!
I have finally finished writing up the notes on the twin
prime conjecture. Click here for a
copy of these notes. I *might* add a homework problem or two about
the combinatorial sieve, and will let you know in the next lecture
in any case.
Click here for a
copy of the second homework set.
Click here for a
copy of the third homework set.
Click here for a copy of
homework 4.
Click here for some notes
on Meinardus's theorem.
(This was a royal pain to write up,
and was a relief when I finished it!)
Click here for some notes on
Stepanov's method.
Click here for a copy of homework 5.
Click here for an intuitive outline
of the proof of the ThueSiegel theorem. There is much more material in
this note than I was willing to cover in class.
Click here for a copy of homework 6.
Click here for notes
on the large sieve and Weyl's estimates. (We may discuss Weyl estimates
again before the term is over.)
Click here for a note
on Szemeredi and HeathBrown's method for sharpening Roth's theorem.
This note was written by Ben Green, and it is explained from a slightly
different perspective than how Szemeredi and HeathBrown formulated their
original proofs.
Click here for a copy of homework 7.
Click here for a
survey article by Andrew Granville on various results in additive
combinatorics.
In my haste to get through the proof of Freiman's Theorem, I
think I could have explained certain details better. Click
here for a five page writeup of some
of these details.
Click here for a note (by Ben Green) on the
BourgainKatzTao sumproduct inequality in F_p.