Pre-talk at 3pm: Properties of the Riemann zeta function"

Main talk at 4pm, Abstract:

In this talk I will discuss two loosely related results about the zeros of $L$-functions. The first result is a proof of a generalization of Newman's conjecture. This conjecture may be viewed as a quantitative version of the statement that the generalized Riemann hypothesis, if true, is only barely so. The second result concerns irregularities in the vertical distribution of the zeros of the Riemann zeta function. The number of zeros of the zeta function up to a given height is estimated by the Riemann-von Mangoldt formula, but the error term in this formula is known to get somewhat large. I will discuss what is known about the distribution of this error term and prove a new lower bound on the tails of this distribution.

Zoom link:

https://umich.zoom.us/j/95185733075

Meeting ID: 951 8573 3075
Passcode: umrtg Speaker(s): Alex Dobner (UCLA)