On the linear independence of Dirichlet L-values

Contact: Pieter Moree (moree@mpim-bonn.mpg.de)

It is an open question of Baker whether 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 also investigate the linear independence of such values at integers
greater than 1.