# Number Theory Seminar

Tuesday, November 12, 2019 — 1:30 PM EST

Arpita Kar, Queen's University

"Some reflections on the Riemann Hypothesis"

In this talk, we will first explore some probabilistic interpretations of the Riemann Hypothesis. In 1997, Xian-Ji Li showed that the Riemann Hypothesis holds if and only if $\lambda_n = \sum_{\rho} \left( 1 - \left(1 - {1 \over \rho}\right)^n\right),$ has $\lambda_n >0$ for $n = 1, 2, 3, ...$, where $\rho$ runs over the complex zeroes of the Riemann zeta function. In this context, we will revisit an important arithmetic formula for these $\lambda_n$-s derived by  Bombieri and Lagarias and see how we can relate it to an expression involving Laguerre polynomials. This is joint work with Prof. Ram Murty.

MC 5417

### November 2019

S M T W T F S
27
28
29
30
31
1
2
3
4
8
9
10
11
15
16
17
19
20
22
23
24
25
26
27
28
29
30
1. 2019 (177)
1. November (11)
2. October (19)
3. September (13)
4. August (7)
5. July (12)
6. June (18)
7. May (22)
8. April (11)
9. March (25)
10. February (17)
11. January (22)
2. 2018 (219)
1. December (2)
2. November (32)
3. October (27)
4. September (26)
5. August (4)
6. July (9)
7. June (13)
8. May (17)
9. April (13)
10. March (28)
11. February (27)
12. January (21)
3. 2017 (281)
4. 2016 (335)
5. 2015 (209)
6. 2014 (235)
7. 2013 (251)
8. 2012 (135)