Notes

• Notes from my analytic number theory course at NTNU: 

Topics in analytic number theory 

Material includes: gaps between zeros of the zeta function (Montgomery-Odlyzko method), large values of GCD sums and the resonance methods of Soundararajan and Bondarenko-Seip, moments of the Riemann zeta function - second and fourth moment asymptotics, conditional upper bounds and conjectures for higher moments. 

• A note on the recent upper bound methods for moments of L-functions: 

Sharp bounds for moments of L-functions

This goes over the methods of Harper and Radziwiłł--Soundararajan which give sharp conditional and unconditional (resp.) upper bounds for moments of L-functions. In particular, I try to motivate and hopefully explain the more tricky "splitting" idea of these arguments.