#### 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

Done