18 citations · 99 across the 31 of their papers we have counts for
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The Minkowski question mark function: explicit series for the dyadic period function and moments
Giedrius Alkauskas
Previously, several natural integral transforms of the Minkowski question mark function F(x) were introduced by the author. Each of them is uniquely characterized by certain regula…
Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]
Giedrius Alkauskas
In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is…
One curious proof of Fermat's little theorem
Giedrius Alkauskas
We give a proof of Fermat's little theorem which does not use nor arithmetic(Euclidean algorithm) neither algebra (group theory), but it rather employs the field of the formal powe…
Generating and zeta functions, structure, spectral and analytic properties of the moments of Minkowski question mark function
Giedrius Alkauskas
In this paper we are interested in moments of Minkowski question mark function ?(x). It appears that, to certain extent, the results are analogous to the results obtained for objec…
Statistical properties of the Calkin--Wilf tree: real an p-adic distribution
Giedrius Alkauskas, Jörn Steuding
We examine statistical properties of the Calkin--Wilf tree and give number-theoretical applications.
The moments of Minkowski question mark function: the dyadic period function
Giedrius Alkauskas
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 g…