We are delighted to welcome Neelam Kandhil (soon to become Dr. Neelam Kandhil) of IMSc, Chennai for our next talk. The talk announcement is below.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
It is an open question of Baker whether the numbers $L(1, \chi)$ for non-trivial Dirichlet characters $\chi$ with period $q$ are linearly independent over $\mathbb{Q}$. The best known result is due to Baker, Birch and Wirsing which affirms this when $q$ is co-prime to $\varphi(q)$. In this talk, we will discuss an extension of this result to any arbitrary family of moduli. The interplay between the resulting ambient number fields brings in new technical issues and complications hitherto absent in the context of a fixed modulus. In the process, we also extend a result of Okada about linear independence of the cotangent values over $\mathbb{Q}$ as well as a result of Murty-Murty about ${\overline{\mathbb{Q}}}$ linear independence of such $L(1, \chi)$ values.
If time permits, we will also discuss the interrelation between the non-vanishing of Dedekind zeta values and its derivatives.
