Integral transforms of the Minkowski question mark function

Alkauskas, Giedrius (2008) Integral transforms of the Minkowski question mark function. PhD thesis, University of Nottingham.

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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.

Item Type:Thesis (PhD)
Supervisors:Fesenko, I.B.
Uncontrolled Keywords:Minkowski question mark function, period functions, Farey tree, moments of the distribution, continued fractions
Faculties/Schools:UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:641
Deposited By:Giedrius Alkauskas
Deposited On:19 Dec 2008
Last Modified:06 Feb 2009 14:44

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