Abstract/Summary

In this paper we study various "abscissae" which one can associate to a given function $f$, or rather to the power moments of $f$. These are motivated by long standing open problems in analytic number theory. We show how these abscissae connect to the distribution of values of $f$ in a very elegant way using convex conjugates. This connection allows us to show which abscissae are realizable for both general and more specific arithmetical functions. Further it may give a new approach to, for example, Dirichlet's divisor problem.