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Power moments and value distribution of functions

Hilberdink, T. (2019) Power moments and value distribution of functions. Transactions of the American Mathematical Society, 371. pp. 1-31. ISSN 1088-6850

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To link to this item DOI: 10.1090/tran/7581


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.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:76912
Publisher:American Mathematical Society


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