#### RG Analysis and Partial Differential Equations

#### 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

### 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.## News

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