Power moments and value distribution of functions

Hilberdink, Titus

doi:10.1090/tran/7581

Power moments and value distribution of functions
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Trans. Amer. Math. Soc. 371 (2019), 1-31 Request permission

Abstract:

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.

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