The Lazard formal group, universal congruences and special values of zeta functions

Abstract

A connection between the theory of formal groups and arithmetic number theory is established. In particular, it is shown how to construct general Almkvist–Meurman–type congruences for the universal Bernoulli polynomials that are related with the Lazard universal formal group (based on earlier works of the author). Their role in the theory of L L –genera for multiplicative sequences is illustrated. As an application, sequences of integer numbers are constructed. New congruences are also obtained, useful to compute special values of a new class of Riemann–Hurwitz–type zeta functions.