Title/Abstract

Talk 2.

Speaker : Ade Irma Suriajaya

Title : Pair correlation of zeros of the Riemann zeta-function: simple zeros and zeros on the critical line 

Abstract : Montgomery (1973) suggested an approach to study the pair correlation of nontrivial zeros of the Riemann zeta-function, and proved the corresponding asymptotic formula within a limited range assuming the Riemann Hypothesis (RH). The extended behavior remains a conjecture which implies the famous Pair Correlation Conjecture (PCC) for these zeros. In my previous work with Siegfred Alan C. Baluyot, Daniel Alan Goldston, and Caroline L. Turnage-Butterbaugh, we have showed how to remove RH in such pair correlation methods and recover Montgomery results on the proportion of simple zeros under hypotheses weaker than RH. We have in addition obtained the proportion of zeros lying on the critical line, which we simply call critical zeros for brevity. In a follow-up work with Daniel Goldston, Junghun Lee and Jordan Schettler, we showed that PCC without RH implies that asymptotically 100% of the zeros are simple and critical, thus RH is asymptotically true. In this talk, I introduce these results and briefly explain our key ideas. 

Talk 4.

Speaker : Ade Irma Suriajaya: 

Title : The pair correlation method of zeros of the Riemann zeta-function: the Alternative Hypothesis 

Abstract : Following up on the previous talk, we can also apply the latter method to other pair correlation conjectures as well, such as the Alternative Hypothesis (AH). AH first arose as a consequence of the possible existence of Landau-Siegel zeros of real Dirichlet L-functions, as demonstrated by D. R. Heath-Brown at a 1996 AIM conference. In this second talk I would like to introduce some ideas behind AH and how to adapt our ideas to AH and obtain the same proportions of simple and critical zeros.