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

  • Monday, 14:15 - 16:00, Zoom
  • Preliminary meeting: Th, 2021-02-11, 16:00, Zoom
We meet in this Zoom room.

Topics

Topics that are not marked with (taken) are available.
  1. Lagarias, Jeffrey C. (1-ATT3) An elementary problem equivalent to the Riemann hypothesis. Amer. Math. Monthly 109 (2002), no. 6, 534–543. (taken)
  2. Barrett, Wayne W. (1-BYU); Forcade, Rodney W. (1-BYU); Pollington, Andrew D. (1-BYU) 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. 15A36 (05C99 11C20 11M26) 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 (3-QEN); Tao, Terence (1-UCLA) 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 19: Topic 1
  • April 26: 2
  • May 3: 3
  • May 10: 4
  • May 17: 5
  • May 31: 5
  • June 7: 6
  • June 14: 7