Geodesic
THE MOMENTS OF MINKOWSKI QUESTION MARK FUNCTION: THE DYADIC PERIOD FUNCTION
Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 41-64

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The Minkowski question mark function ?(x) arises as a real distribution of rationals in the Farey tree. We examine the generating function of moments of ?(x). It appears that the generating function is a direct dyadic analogue of period functions for Maass wave forms and it is defined in the cut plane \ (1, ∞). The exponential generating function satisfies an integral equation with kernel being the Bessel function. The solution of this integral equation leads to the definition of dyadic eigenfunctions, arising from a certain Hilbert–Schmidt operator. Finally, we describe p-adic distribution of rationals in the Stern–Brocot tree. Surprisingly, the Eisenstein series G2(z) does manifest in both real and p-adic cases.
DOI : 10.1017/S0017089509990152
Mots-clés : Primary – 11A55, 26A30, 11F03, Secondary – 33C10 
ALKAUSKAS, GIEDRIUS. THE MOMENTS OF MINKOWSKI QUESTION MARK FUNCTION: THE DYADIC PERIOD FUNCTION. Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 41-64. doi: 10.1017/S0017089509990152
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     title = {THE {MOMENTS} {OF} {MINKOWSKI} {QUESTION} {MARK} {FUNCTION:} {THE} {DYADIC} {PERIOD} {FUNCTION}},
     journal = {Glasgow mathematical journal},
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     year = {2010},
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