Plan for the study group

We will study old and new developments regarding the distribution of values of L-functions including some recent breakthroughs towards the Fyodorov-Hiary-Keating Conjecture.

The study group will run from April 21-June 30 and meets on Wednesdays from 14:30-15:30 (UK time) on Zoom. An email with the link to the meeting will be sent to all participants. If you would like to participate in the study group please contact one of the organizers below.

The program for the study group consists of two parts

Part I (April 21-June 9): Survey of old and new developments on the distribution of L-functions. The program is below.

Part II (June 16-): An in depth study of a recent breakthrough towards the Fyodorov-Hiary-Keating conjecture:

"Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line"

We will read the above paper, going through the details of the proofs.

Organizers: Steve Lester (King's College), Igor Wigman (King's College)

Program for Part I

• April 21, Topic: The distribution of values of the Riemann zeta-function inside the critical strip

Speaker: Anurag Sahay (University of Rochester)

• April 28, Topic: The distribution of extreme values of L(1,χ_d)

Speaker: Felicien Comtat (Queen Mary University of London)

• May 5, Topic: Selberg's Central Limit Theorem

Speaker: Fatma Cicek (IIT Gandhinagar)

• May 12, Topic: Upper bounds for moments of L-functions

Speaker: Marios Voskou (University College London)

• May 26, Topic: Lower bounds for moments of L-functions

Speaker: Tim Davis (Queen Mary University of London)

• June 2, Topic: Gonek, Hughes, and Keating's hybrid Euler-Hadamard product for L-functions

Speaker: Michael Yiasemides (University of Exeter)

• June 9, Topic: Radziwill and Soundararajan's work on the distribution of central L-values of quadratic twists of elliptic curves

Speaker: Natalie Evans (King's College London)

Program for Part 2

• June 16, Topic: The Fyodorov-Hiary-Keating Conjecture: Sections 1-3 of "Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line"

Speaker: Jesse Jääsaari (Queen Mary University of London)

• June 23, Topic: The Fyodorov-Hiary-Keating Conjecture: Section 4 of "Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line"

Speaker: Natalie Evans (King's College London)

• June 30, Topic: The Fyodorov-Hiary-Keating Conjecture: Section 5 of "Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line"

Speaker: Kevin Kwan (Columbia University)