Alladi Ramakrishnan Hall

Around non-vanishing, transcendence and linear independence of L values at rational and integer points

Neelam Kandhil

IMSc

It is an open question of Baker whether the Dirichlet L values at 1 with fixed modulus are linearly independent over the rational numbers. The best known result is due to Baker, Birch and Wirsing, which affirms this when the modulus of the associated Dirichlet character is co-prime to its Euler's phi value. 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 new technical issues and complications hitherto absent in the context of a fixed modulus. We will investigate the linear independence of such values at integers greater than 1, and the interrelation between the non-vanishing of Dedekind zeta values and their derivatives. If time permits, we will also outline some of the proofs.