Number Theory Seminar

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