M1 Grant for Wadim Zudilin

The vast majority of real numbers are irrational, that is, they cannot be written as quotients of two integers. The number π = 3.1415926. . . , which is defined as the ratio of a circle’s circumference to its diameter, is one such notable example. But for many other mathematically famous quantities, like the values of Riemann’s zeta function at odd positive integers, the irrationality remains a difficult open problem. The proposed project is aimed at solving such challenges and creating new methods to be used in other areas of mathematics.