Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.514718
Title: Integral transforms of the Minkowski question mark function
Author: Alkauskas, Giedrius
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2008
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Abstract:
The Minkowski question mark function F(x) arises as a real distribution function of rationals in the Farey (alias, Stern-Brocot or Calkin-Wilf) tree. In this thesis we introduce its three natural integral transforms: the dyadic period function G(z), defined in the cut plane; the dyadic zeta function zeta_M(s), which is an entire function; the characteristic function m(t), which is an entire function as well. Each of them is a unique object, and is characterized by regularity properties and a functional equation, which reformulates in its own terms the functional equation for F(x). We study the interrelations among these three objects and F(x). It appears that the theory is completely parallel to the one for Maass wave forms for PSL_2(Z). One of the main purposes of this thesis is to clarify the nature of moments of the Minkowski question mark function.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.514718  DOI: Not available
Keywords: QA611 Topology
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