On the arithmetic mean of the size of cross-union families

Acta Mathematica Hungarica - Let $$n > k > 1$$ be integers, $$[n] = \{1, \ldots, n\}$$ the standard $$n$$ -element set and $${[n]\choose k}$$ the collection of all its $$k$$ -subsets....     

A note on lower bounds of heights of non-zero Fourier coefficients of Hilbert cusp forms

Archiv der Mathematik - It is a conjecture of Atkin and Serre that for any $$\epsilon > 0$$, there exists a constant $$c(\epsilon ) > 0$$ such that the Ramanujan $$\tau $$-function...     

The length and depth of algebraic groups

Mathematische Zeitschrift - Let G be a connected algebraic group. An unrefinable chain of G is a chain of subgroups $$G = G_0> G_1> \cdots > G_t = 1$$ , where each $$G_i$$ is a...     

A ternary Diophantine inequality with prime numbers of a special form

Periodica Mathematica Hungarica - Let N be a sufficiently large real number. In this paper, we prove that, for $$1<\frac{973}{856}$$ and for any arbitrarily large number $$E>0$$ , the...     

An application of Baker’s method to the Jeśmanowicz’ conjecture on primitive Pythagorean triples

Periodica Mathematica Hungarica - Let m, n be positive integers such that $$m>n$$, $$\gcd (m,n)=1$$ and $$m \not \equiv n \pmod {2}$$. In 1956, L. Je?manowicz conjectured that...     

Multiple expansions of real numbers with digits set $$\left\{ 0,1,q\right\} $$ 0 , 1 , q

Mathematische Zeitschrift - For $$q>1$$ we consider expansions in base q with digits set $$\left\{ 0,1,q\right\} $$ . Let $${{\mathcal {U}}}_q$$ be the set of points which have a unique...     

3-rank of ambiguous class groups of cubic Kummer extensions

Periodica Mathematica Hungarica - Let $$k=k_0(\root 3 \of {d})$$ be a cubic Kummer extension of $$k_0=\mathbb {Q}(\zeta _3)$$ with $$d>1$$ a cube-free integer and $$\zeta _3$$ a primitive...     

On $${\mathcal {I}}_{

Tóth  János T.  Filip  Ferdinánd  Bukor  József  Zsilinszky  László 《Periodica Mathematica Hungarica》2021,82(2):125-135

Prime-representing functions and Hausdorff dimension

Acta Mathematica Hungarica - Let $$c \geq 2$$ be any fixed real number. Matomäki [4] inverstigated the set of $$A > 1$$ such that the integer part of $$ A^{c^k}$$ is a prime number for...     

Sparse graphs and an augmentation problem

Mathematical Programming - For two integers $$k>0$$ and $$\ell $$ , a graph $$G=(V,E)$$ is called $$(k,\ell )$$ -tight if $$|E|=k|V|-\ell $$ and $$i_G(X)\le k|X|-\ell $$ for each...     

A note on the exceptional solutions of Jeśmanowicz’ conjecture concerning primitive Pythagorean triples

Periodica Mathematica Hungarica - Let $$(m,\ n)$$ be fixed positive integers such that $$m>n,\ \gcd (m,\ n)=1$$ and $$ mn\equiv 0 \pmod 2$$ . Then the triple $$(m^2-n^2,\ 2mn,\ m^2+n^2)$$ is...     

Fractional Parts of Noninteger Powers of Primes

Mathematical Notes - Let $$\alpha > 0$$ be any fixed noninteger. In the paper, we prove an analogue of the Bombieri–Vinogradov theorem for the set of primes $$p$$ satisfying the...     

Jacobi Fields and Conjugate Points for a Projective Class of Sprays

Mediterranean Journal of Mathematics - For the perimeter P(a, b) of an ellipse with the semi-axes $$a\ge b>0$$ , a sequence $$P_n(a,b)$$ is constructed such that the relative error...     

Sharp bounds for the q-gamma function in terms of the Lambert W function

The Ramanujan Journal - In this paper, the function $$F_a(x;q)$$ is defined in terms of logarithmic of q-gamma function for all reals x, a and q with $$q>0$$ . The values of a in...     

P-Laplace Equation for the Grushin Type Operator

Acta Mathematica Sinica, English Series - Let Gλ, λ > 0, be a Grushin type operator on $$\mathbb{R}^{n}\times\mathbb{R}^{m}$$ . In this paper, we will first establish existence and...     

A note on Linnik’s theorem on quadratic non-residues

Archiv der Mathematik - We present a short and purely combinatorial proof of Linnik’s theorem: for any $$\varepsilon >0$$ there exists a constant $$C_\varepsilon $$ such that for any...     

Steklov convexification and a trajectory method for global optimization of multivariate quartic polynomials

Mathematical Programming - The Steklov function $$\mu _f(\cdot ,t)$$ is defined to average a continuous function f at each point of its domain by using a window of size given by $$t>0$$ . It...     

On the Solvability of Riemann Problems in Grand Hardy Classes

Mathematical Notes - The grand Hardy classes $$H_{p)}^{+}$$ and $${}_{m}H_{p)}^{-}$$ , $$p>1$$ , of functions analytic inside and outside the unit disk, which are generated by the norms of...     

Joint Universality of Certain Dirichlet Series

Mathematical Notes - In this paper, we define the Dirichlet series $$ \zeta_{u_T j} (s)$$ , $$ j = 1, \dots, r$$ , absolutely converging in the half-plane $$ \operatorname{Re} s> 1/2 $$ and...     

Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order $$k=3$$

Theoretical and Mathematical Physics - We study fertile hard-core models with three states and an activity parameter $$\lambda>0$$ on the Cayley tree of order $$k=3$$ . It is known that...