The Minkowski ?(x) function and Salem's problem

Details The Minkowski ?(x) function and Salem's problem The Minkowski ?(x) function and Salem's problem

2012-01-31

arxiv.org/abs/1201.6539v1

C. R. Acad. Sci. Paris, Ser. I. 350 (3-4) (2012), 137-140

Mathematics

Number Theory

4 pages. C. R. Acad. Sci. Paris, Ser. I. (2012)

Scientific paper

10.1016/j.crma.2012.01.012

R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943) 427-439) asked whether the Fourier-Stieltjes transform of the Minkowski question mark function ?(x) vanishes at infinity. In this note we present several possible approaches towards the solution. For example, we show that this transform satisfies integral and discrete functional equations. Thus, we expect the affirmative answer to Salem's problem. In the end of this note we show that recent attempt to settle this question (S. Yakubovich, C. R. Acad. Sci. Paris, Ser. I 349 (11-12) (2011) 633-636) is fallacious.

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