# Browse Our Mathematics and Statistics Journals

Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.

# Mathematics and Statistics

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# Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function

Studia Scientiarum Mathematicarum Hungarica
Author: Antanas Laurinčikas

## Abstract

Let 0 < γ 1 < γ 2 < ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function ζ(s + k h, α), h > 0, with parameter α such that the set {log(m + α): m$ℕ0$} is linearly independent over the field of rational numbers. For this, a weak form of the Montgomery conjecture on the pair correlation of {γ k} is applied.

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# Characterization of automorphisms of twisted tensor biproducts

Studia Scientiarum Mathematicarum Hungarica
Authors: Wang Xing, Chen Quanguo, and Wang Dingguo

## Abstract

We study certain subgroups of the full group of Hopf algebra automorphisms of twisted tensor biproducts.

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# The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

Studia Scientiarum Mathematicarum Hungarica
Authors: Tahir S. Gadjiev, Vagif S. Guliyev, and Konul G. Suleymanova

## Abstract

In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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# The first cohomology group of some operator algebras on Hilbert C*-modules

Studia Scientiarum Mathematicarum Hungarica
Authors: Hoger Ghahramani and Saman Sattari

## Abstract

Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C*-module X called operator algebras with property $k$ and operator algebras with property ℤ, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.

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# Integral bases of pure fields with square-free parameter

Studia Scientiarum Mathematicarum Hungarica
Author: László Remete

## Abstract

Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type $ℚ(nm)$ is explicitly known for n = 2, 3,4. It is well known that for n = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases.

In this paper we explicitly give an integral basis of the field $ℚ(nm)$, where m ≠ ±1 is square-free. Furthermore, we show that similarly to the quadratic case, an integral basis of $ℚ(nm)$ is repeating periodically in m with period length depending on n.

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# Jordan's totient function and trigonometric sums

Studia Scientiarum Mathematicarum Hungarica
Author: Wenchang Chu

## Abstract

Two classes of trigonometric sums about integer powers of secant function are evaluated that are closely related to Jordan's totient function.

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# An L-function free proof of Hua's Theorem on sums of five prime squares

Studia Scientiarum Mathematicarum Hungarica
Author: Claus Bauer

## Abstract

We provide a new proof of Hua's result that every sufficiently large integer N ≡ 5 (mod 24) can be written as the sum of the five prime squares. Hua's original proof relies on the circle method and uses results from the theory of L-functions. Here, we present a proof based on the transference principle first introduced in[5]. Using a sieve theoretic approach similar to ([10]), we do not require any results related to the distributions of zeros of L- functions. The main technical difficulty of our approach lies in proving the pseudo-randomness of the majorant of the characteristic function of the W-tricked primes which requires a precise evaluation of the occurring Gaussian sums and Jacobi symbols.

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# Character varieties of even classical pretzel knots

Studia Scientiarum Mathematicarum Hungarica
Author: Haimiao Chen

## Abstract

For each even classical pretzel knot P(2k 1 + 1, 2k 2 + 1, 2k 3), we determine the character variety of irreducible SL (2, ℂ)-representations, and clarify the steps of computing its A-polynomial.

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# A Construction of Cohen-Macaulay Graphs

Studia Scientiarum Mathematicarum Hungarica
Authors: Safyan Ahmad and Shamsa Kanwal

## Abstract

We present a technique to construct Cohen–Macaulay graphs from a given graph; if this graph fulfills certain conditions. As a consequence, we characterize Cohen–Macaulay paths.

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# Domain representable Lindelöf spaces are cofinally Polish

Studia Scientiarum Mathematicarum Hungarica
Author: Vladimir V. Tkachuk

## Abstract

We prove that, for any cofinally Polish space X, every locally finite family of non-empty open subsets of X is countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class of σ-compact spaces. It turns out that, for a topological group G whose space has the Lindelöf Σ-property, the space G is domain representable if and only if it is Čech-complete. Our results solve several published open questions.

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