scholarly journals On the derivative of iterations of the Minkowski question mark function at special points

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Nikita Shulga
Keyword(s):  
Question Mark ◽  
Special Points ◽  
Minkowski Question Mark Function

scholarly journals On the affirmative solution to Salem’s problem

Analysis ◽  
2019 ◽  
Vol 39 (4) ◽  
pp. 135-149
Author(s):  
Semyon Yakubovich
Keyword(s):  
Linear Combination ◽  
Special Functions ◽  
Type Problem ◽  
Classical Analysis ◽  
Question Mark ◽  
Affirmative Solution ◽  
Minkowski Question Mark Function ◽  
Stieltjes Transforms

Abstract The Salem problem to verify whether Fourier–Stieltjes coefficients of the Minkowski question mark function vanish at infinity is solved recently affirmatively. In this paper by using methods of classical analysis and special functions we solve a Salem-type problem about the behavior at infinity of a linear combination of the Fourier–Stieltjes transforms. Moreover, as a consequence of the Salem problem, some asymptotic relations at infinity for the Fourier–Stieltjes coefficients of a power {m\in\mathbb{N}} of the Minkowski question mark function are derived.

scholarly journals Diophantine properties of fixed points of Minkowski question mark function

2020 ◽  
Vol 195 (4) ◽  
pp. 367-382
Author(s):  
Dmitry Gayfulin ◽  
Nikita Shulga
Keyword(s):  
Fixed Points ◽  
Question Mark ◽  
Minkowski Question Mark Function

scholarly journals THE MOMENTS OF MINKOWSKI QUESTION MARK FUNCTION: THE DYADIC PERIOD FUNCTION

2009 ◽  
Vol 52 (1) ◽  
pp. 41-64 ◽  
Author(s):  
GIEDRIUS ALKAUSKAS
Keyword(s):  
Integral Equation ◽  
Generating Function ◽  
Period Function ◽  
Question Mark ◽  
Real Distribution ◽  
Exponential Generating Function ◽  
Wave Forms ◽  
Schmidt Operator ◽  
Definition Of ◽  
Minkowski Question Mark Function

AbstractThe 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.

scholarly journals Differentiability of the Minkowski question mark function

2013 ◽  
Vol 401 (2) ◽  
pp. 774-794 ◽  
Author(s):  
Anna A. Dushistova ◽  
Igor D. Kan ◽  
Nikolay G. Moshchevitin
Keyword(s):  
Question Mark ◽  
Minkowski Question Mark Function
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