On the dimension of Chowla–Milnor space

Abstract

In a recent work, Gun, Murty and Rath defined the Chowla–Milnor space and proved a non-trivial lower bound for these spaces. They also obtained a conditional improvement of this lower bound and noted that an unconditional improvement of their lower bound will lead to irrationality of ζ(k)/ π ^k for odd positive integers k > 1. In this paper, we give an alternate proof of their theorem about the conditional lower bound.