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arXiv · 1308.6448

The Strong Chowla-Milnor spaces and a conjecture of Gun, Murty and Rath

Tapas Chatterjee
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Abstract

In a recent work, Gun, Murty and Rath formulated the Strong Chowla-Milnor conjecture and defined the Strong Chowla-Milnor space. In this paper, we prove a non-trivial lower bound for the dimension of these spaces. We also obtain a conditional improvement of this lower bound and noted that an unconditional improvement of this lower bound will lead to irrationality of both $ζ(k)$ and $ζ(k)/ π^k$ for all odd positive integers $k>1$. Following Gun, Murty and Rath, we define generalized Zagier spaces $V_p(K)$ for multiple zeta values over a number field $K$. We prove that the dimension of $V_{4d+2}(K)$ for $d\geq 1$, is at least 2, assuming a conjecture of Gun, Murty and Rath.

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Tapas Chatterjee. 2013-08-29. The Strong Chowla-Milnor spaces and a conjecture of Gun, Murty and Rath. https://arxiv.org/abs/1308.6448

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