### Moments of L-functions and the Density Hypothesis

Linfoot Number Theory Seminar

15th February 2023, 11:00 am – 12:00 pm

Fry Building, Room 2.04

The Density Hypothesis is a long-standing open problem concerning the density of zeros of L-functions in the critical strip, and in some contexts it is as strong as the Riemann Hypothesis. One method for proving zero-density theorems involves finding asymptotic formulae for mollified moments and optimising the mollifier. Increasing the length of the mollifier can strengthen the result, however there are some natural barriers to overcome. In this talk we break one of these barriers to find an asymptotic formula for the twisted second moment of Dirichlet L-functions in two aspects, and use it to prove a zero-density theorem.

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