Title:
Lambda-rings and multiplicative functions
Abstract:
This is joint work with Ane Espeseth and Torstein Vik. We show that many
important classes of elementary multiplicative functions can be endowed with
a lambda-ring structure in a natural way. In these structures, the addition is
given by Dirichlet convolution, the multiplication is given by a certain
"deformation" of the pointwise multiplication, and the Adams operations can
in some cases be identified with operations known under other names in the
literature. This leads to an elementary but very pleasant framework for a
systematic understanding of many classical identities between multiplicative
functions. The first part of the talk will consist of a general introduction to
lambda-rings.