THE LAZARD FORMAL GROUP, UNIVERSAL CONGRUENCES AND SPECIAL VALUES OF ZETA FUNCTIONS

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-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.