Related papers: A new proof of a theorem of Tietze
For integers $m \geq 2$, we study divergent continued fractions whose numerators and denominators in each of the $m$ arithmetic progressions modulo $m$ converge. Special cases give, among other things, an infinite sequence of divergence…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
We prove an infinitary version of the Brauer-Schur theorem.
As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.
We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^\ast$-correspondences, and has several applications.
In this paper, we prove the semi-continuity theorem of Diederich-Forn{\ae}ss index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
We determine the Lebesgue measure and Hausdorff dimension of various sets of real numbers with infinitely many partial quotients that are both large and prime, thus extending the well-known theorems by {\L}uczak (1997) and Huang-Wu-Xu…
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
We extend almost everywhere convergence in Wiener-Wintner ergodic theorem for $\sigma$-finite measure to a generally stronger almost uniform convergence and present a larger, universal, space for which this convergence holds. We then extend…
We prove the equidistribution of subsets of $(\Rr/\Zz)^n$ defined by fractional parts of subsets of~$(\Zz/q\Zz)^n$ that are constructed using the Chinese Remainder Theorem.
In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…
New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and…
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.
We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.
We prove an analog of Siegel's theorem for integral points in the context of Drinfeld modules. The result holds for finitely generated submodules of the additive group over a function field of transcendence dimension 1.