Mathematisches Institut der Universität Bonn

Arbeitsgruppe Analysis und Partielle Differentialgleichungen

Summer term 2021

S4B1 - Graduate Seminar on Analysis

Analytic Approaches to the Riemann Hypothesis

Instructors

Dr. Felipe Gonçalves, PD Dr. Pavel Zorin-Kranich.

Dates

• Tuesday, 8:15 - 10:00
• Preliminary meeting: Th, 2021-02-11, 16:00
• First meeting at a different time: Mo, 2021-04-12, 14:15 - 16:00

We meet in this Zoom room. In order to prevent vandalism, you must be logged into your @uni-bonn.de account in Zoom to join the meeting, see here for instructions (section "Registrieren als Host für Veranstaltungen").

Topics

Topics that are not marked with (taken) are available.

1. Lagarias, Jeffrey C. - An elementary problem equivalent to the Riemann hypothesis. Amer. Math. Monthly 109 (2002), no. 6, 534–543. (taken)
2. Barrett, Wayne W.; Forcade, Rodney W.; Pollington, Andrew D. - On the spectral radius of a (0,1) matrix related to Mertens' function. Proceedings of the Victoria Conference on Combinatorial Matrix Analysis (Victoria, BC, 1987). Linear Algebra Appl. 107 (1988), 151–159. Note: student should explain a little bit about why sum(j=1,n,mu(n)) << n^(1/2+epi) is equivalent to RH. (taken)
3. Levinson, Norman - More than one third of zeros of Riemann's zeta-function are on σ=1/2 Advances in Math. 13 (1974), 383–436. Note: Simpler and more accessible expositions given by Young [MR2745463] and Bombieri [MR0444585]. Note: Comment that Conrey has the best result essentially: 40%. (taken)
4. Beurling-Nyman Criterion Chapter 3 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents. see also: https://www.esi.ac.at/static/esiprpr/esi623.pdf
5. Rodgers, Brad; Tao, Terence - The de Bruijn–Newman constant is non-negative. Forum Math. Pi 8 (2020), e6, 62 pp. 2 students. See chapter 5 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents for more background. (taken)
6. Integral Equations Chapter 8 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents. 8.1-8.4 (not 8.5)
7. Michael Griffin, Ken Ono, Larry Rolen, Don Zagier - Jensen polynomials for the Riemann zeta function and other sequences (taken)

Dates

• April 12: Felipe
• April 20: Topic 1
• April 27: 2
• May 4: 3
• May 11: 4
• May 18: 5
• June 1: 5
• June 15: 7 - canceled
• June 22: 8
• July 6: 6

Talk preparation

Contact Felipe to discuss your topic at least a week before your presentation date.