Power moments and value distribution of functions
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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.References
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Additional Information
- Titus Hilberdink
- Affiliation: Department of Mathematics, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, United Kingdom
- MR Author ID: 603983
- Email: t.w.hilberdink@reading.ac.uk
- Received by editor(s): July 11, 2016
- Published electronically: September 20, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 1-31
- MSC (2010): Primary 11N64, 52A41
- DOI: https://doi.org/10.1090/tran/7581
- MathSciNet review: 3885136