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.
- Lagarias, Jeffrey C. -
An elementary problem equivalent to the Riemann hypothesis.
Amer. Math. Monthly 109 (2002), no. 6, 534–543.
(taken)
- 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)
- 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)
- 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
- 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)
- Integral Equations
Chapter 8 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents.
8.1-8.4 (not 8.5)
- 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.
