Acta Mathematica Hungarica最新文献

We classify all the (n)-component links in the (3)-sphere that bounda Thurston norm minimizing Seifert surface (Sigma) with Euler characteristic (chi(Sigma)=n-2) and that are nearly fibered, which means that the rank of their link Floerhomology group (widehat{HFL}) in the maximal (collapsed) Alexander grading (s_{text{top}}) is equalto two. In other words, such a link (L) satisfies (s_{text{top}}=frac{n-chi(Sigma)}{2}=1), and in addition ({rm rk}widehat{HFL}_{*}(L)[1]=2) and ({rm rk}widehat{HFL}_{*}(L)[s]=0) for every (s>1).

The proof of the main theorem is inspired by the one of a similar recent result for knots by Baldwin and Sivek, and involves techniques from sutured Floerhomology. Furthermore, we also compute the group (widehat{HFL}) for each of these links.

Let p^a be a prime power and n₀ a square-free number. We prove that any complementing pair in a cyclic group of order p^an₀ is quasi-periodic, with one component decomposable by the the subgroup of order p. The proof is by induction and reduction since the presence of the square-free factor n₀ allows us to perform a Tijdeman decomposition. We also give an explicit example to show that (mathbb{Z}_{72}) is the smallest cyclic group that fails to have the strong Tijdeman property.

We characterize the translation invariant monotone collections of multi-dimensional intervals for which the analogue of Stein's criterion for the integrability of the Hardy--Littlewood maximal function is true. Namely, we characterize the collections (B) of the mentioned type for which the conditions (int_{[0,1]^d}M_B(f)<infty) and (int_{[0,1]^d}vert fvert log^+vert fvert <infty) are equivalent for functions (f)supported on the unit cube ([0,1]^d). Here (M_B) denotes the maximal operator associated to a collection (B).

We study the real interpolation spaces between weak martingale Hardy-type spaces (WH_{X}^{s}(Omega)) and martingale Hardy space (H_{infty}^{s}(Omega)) associated with quasi-Banach function lattice by using atomic characterizations of weak martingale Hardy-type spaces. As applications, we obtain the corresponding results on the weighted Lorentz space and the generalized grand Lebesgue space. We point out that even in these special cases, the results obtained in this article are also new.

As a consequence of their work, Bruce C. Berndt, Ronald J. Evans, Larry Joel Goldstein and Michael Razar obtained a formula for the square of the class number of an imaginary quadratic number field in terms of Dedekind sums. We give a short proof of it and also express the relative class numbers of imaginary abelian number fields in terms of Dedekind sums.

Let f and g be two different holomorphic cusp froms or Maass cusp forms for the full modular group (SL(2,mathbb{Z})). We are interested in coefficients of Rankin–Selberg L-functions, and establish some bounds for

and

where (varphi>0) and h is a fixed positive integer.

In 2011, Dekel et al. introduced a highly geometric Hardy spaces (H^p(Theta)), for the full range (0<ple 1), which are constructed over a continuous multilevelellipsoid cover (Theta) of (mathbb{R}^n) with high anisotropy in the sense that the ellipsoidscan change shape rapidly from point to point and from level to level. We introducea new class of fractional integral operators (T_{alpha}) adapted to ellipsoid cover (Theta) andobtained their boundedness from (H^p(Theta)) to (H^q(Theta)) and from (H^p(Theta)) to (L^q(mathbb{R}^n)),where (frac{1}{q}=frac{1}{p}+alpha) and (0<alpha<1).

T. M. Apostol introduced a certain Möbius function (mu_{k}(cdot)) of order k, where (kgeq 2) is a fixed integer. Let k=1,then (mu_{1}(cdot)) coincides with the Möbius function (mu(cdot)), in the usual sense.For any fixed (kgeq 2), he proved the asymptotic formula (sum_{nleq x}mu_{k}(n)=A_{k}x+O_{k}(x^{1/k}log x))as (xtoinfty), where (A_{k}) is a positive constant. Later, under the Riemann Hypothesis, D. Suryanarayana showed the O-term is(O_{k}bigl(x^{frac{4k}{4k^{2}+1}}expbigl(Dfrac{log x}{loglog x}bigr)!bigr))with some positive constant D. In this paper, without using any unproved hypothesis we shall prove thatthe O-term obtained by Apostol can be improved to (O_{k}bigl(x^{1/k}expbigl(-D_{k}frac{(log x)^{3/5}}{(log log x)^{1/5}}bigr)!bigr))with some positive constant (D_{k}).

The concept of zero-divisor graphs of rings is widely used for establishing relationships between the properties of graphs and the properties of the underlying ring. The zero-divisor graph of a ring is generalized to the k-zero-divisor hypergraph of a ring R for (kin mathbb{N}), which is denoted by (mathcal{H}_{k}(R)).This paper is an endeavor to discuss some properties of zero-divisor hypergraphs.We determine the diameter and girth of (mathcal{H}_{k}(R)) whenever R is reduced.Also, we characterize all commutative rings R for which (mathcal{H}_{k}(R)) is in some known class of graphs.Further, we obtain certain necessary conditions for (mathcal{H}_{k}(R)) to be a Hamilton Berge cycle and a flag-traversing tour.Moreover, we answer a case of the question raised by Eslahchi et al. [15].

Let N be a sufficiently large number, (mathfrak{A}) and (mathfrak{B}) be subsets of ({N+1, ldots , 2N}). We prove that if (1<c<frac{6}{5}), (|mathfrak{A}|, |mathfrak{B}|gg N^{2-2delta}) and (delta>0) is sufficiently small, then the equation

is solvable, which improves the result of Rivat and Sárközy [14]. We also investigate the solvability of the equation

where P_k denotes an almost-prime with at most k prime factors and c₀ is a fixed real number depends on k.