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2009 Generating and zeta functions, structure, spectral and analytic properties of the moments of the Minkowski question mark function
Giedrius Alkauskas
Involve 2(2): 121-159 (2009). DOI: 10.2140/involve.2009.2.121

Abstract

In this paper we are interested in moments of the Minkowski question mark function ?(x). It appears that, to some extent, the results are analogous to results obtained for objects associated with Maass wave forms: period functions, L-series, distributions. These objects can be naturally defined for ?(x) as well. Various previous investigations of ?(x) are mainly motivated from the perspective of metric number theory, Hausdorff dimension, singularity and generalizations. In this work it is shown that analytic and spectral properties of various integral transforms of ?(x) do reveal significant information about the question mark function. We prove asymptotic and structural results about the moments, calculate certain integrals which involve ?(x), define an associated zeta function, generating functions, Fourier series, and establish intrinsic relations among these objects.

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Giedrius Alkauskas. "Generating and zeta functions, structure, spectral and analytic properties of the moments of the Minkowski question mark function." Involve 2 (2) 121 - 159, 2009. https://doi.org/10.2140/involve.2009.2.121

Information

Received: 29 January 2008; Accepted: 29 December 2008; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1170.11028
MathSciNet: MR2501334
Digital Object Identifier: 10.2140/involve.2009.2.121

Subjects:
Primary: 11A55, 11M41, 26A30
Secondary: 11F99

Rights: Copyright © 2009 Mathematical Sciences Publishers

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