On linear independence of Dirichlet L-values

Abstract: 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 also investigate the linear independence of such values at integers greater than 1.

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar