IMSc Webinar

Irrationality of zeta(2) by determinantal methods

Krishnan Rajkumar

JNU

We will first recall Apéry's and Beukers' proofs of irrationality
of zeta(2) and zeta(3) and attempt to formulate an "existential" proof of
irrationality using Minkowski's linear forms theorem. We will then outline
the difficulties in using several methods to estimate a determinant at the
heart of this proof including multiple hypergeometric series, vector
equilibrium problems, large deviations and Szegő's limit theorem. We then
change the irrationality criterion to observe that one of these approaches
yields the irrationality of zeta(2). The final part of the talk will be to
attempt to convince the audience that a Selberg-type integral evaluation
exists which will side-step all the above difficulties.
Google meet link: meet.google.com/bfy-buhp-ohf