Related papers: On Fabry's Gap Theorem

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

Turan's theorem implies that every graph of order n with more edges than the r-partite Turan graph contains a complete graph of order r+1. We show that the same premise implies the existence of much larger graphs. We also prove…

We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.

We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.

This is an introductory article to the theory of multiple gaps.

We present a proof of the Sturm-Hurwitz theorem, using basic calculus.

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.

We give a simple and straightforward proof of the Gap Theorem for separated sequences by A. Poltoratski and M. Mitkovski using the Beurling--Malliavin formula for the radius of completeness.

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

The Three Gap Theorem, also known as the Steinhaus Conjecture, is a classical result on the combinatorics of the fractional part function, and has since been generalized in many ways. In this paper, we pose a new problem related to these…

We show that Fueter's theorem holds for a more general class of quaternionic functions than those constructed by the Fueter's method.

The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places $n$ points on a circle, at angles of $z, 2z, 3z, \ldots nz$ from the starting point. The theorem was first proven in 1958 by S\'os and many…

In 2007, \'A. Baricz put forward a conjecture concerning Tur\'an-type inequalities for Gaussian hypergeometric functions (see Conjecture \ref{ConjA} in Section \ref{Sec1}). In this paper, the authors disprove this conjecture with several…

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

This paper presents a generalized version of a theorem of Grzegorek and Labuda in category bases and also endeavours to establish a variant formulation of the same in Marczewski structures.

We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.