Displaying similar documents to “Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial”

On the gaps between q -binomial coefficients

Florian Luca, Sylvester Manganye (2021)

Communications in Mathematics

Similarity:

In this note, we estimate the distance between two q -nomial coefficients n k q - n ' k ' q , where ( n , k ) ( n ' , k ' ) and q 2 is an integer.

On Bernstein inequalities for multivariate trigonometric polynomials in L p , 0 p

Laiyi Zhu, Xingjun Zhao (2022)

Czechoslovak Mathematical Journal

Similarity:

Let 𝕋 n be the space of all trigonometric polynomials of degree not greater than n with complex coefficients. Arestov extended the result of Bernstein and others and proved that ( 1 / n ) T n ' p T n p for 0 p and T n 𝕋 n . We derive the multivariate version of the result of Golitschek and Lorentz T n cos α + 1 n T n sin α l ( m ) p T n p , 0 p for all trigonometric polynomials (with complex coeffcients) in m variables of degree at most n .

L p inequalities for the growth of polynomials with restricted zeros

Nisar A. Rather, Suhail Gulzar, Aijaz A. Bhat (2022)

Archivum Mathematicum

Similarity:

Let P ( z ) = ν = 0 n a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1 , then for 1 p < and R > 1 , Boas and Rahman proved P ( R z ) p ( R n + z p / 1 + z p ) P p . In this paper, we improve the above inequality for 0 p < by involving some of the coefficients of the polynomial P ( z ) . Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.

Global analytic and Gevrey surjectivity of the Mizohata operator D 2 + i x 2 2 k D 1

Lamberto Cattabriga, Luisa Zanghirati (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

The surjectivity of the operator D 2 + i x 2 2 k D 1 from the Gevrey space E s R 2 , s 1 , onto itself and its non-surjectivity from E s R 3 to E s R 3 is proved.

Existence of positive solutions for second order m-point boundary value problems

Ruyun Ma (2002)

Annales Polonici Mathematici

Similarity:

Let α,β,γ,δ ≥ 0 and ϱ:= γβ + αγ + αδ > 0. Let ψ(t) = β + αt, ϕ(t) = γ + δ - γt, t ∈ [0,1]. We study the existence of positive solutions for the m-point boundary value problem ⎧u” + h(t)f(u) = 0, 0 < t < 1, ⎨ α u ( 0 ) - β u ' ( 0 ) = i = 1 m - 2 a i u ( ξ i ) γ u ( 1 ) + δ u ' ( 1 ) = i = 1 m - 2 b i u ( ξ i ) , where ξ i ( 0 , 1 ) , a i , b i ( 0 , ) (for i ∈ 1,…,m-2) are given constants satisfying ϱ - i = 1 m - 2 a i ϕ ( ξ i ) > 0 , ϱ - i = 1 m - 2 b i ψ ( ξ i ) > 0 and Δ : = - i = 1 m - 2 a i ψ ( ξ i ) ϱ - i = 1 m - 2 a i ϕ ( ξ i ) ϱ - i = 1 m - 2 b i ψ ( ξ i ) - i = 1 m - 2 b i ϕ ( ξ i ) < 0 . We show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and...

Meromorphic function sharing a small function with a linear differential polynomial

Indrajit Lahiri, Amit Sarkar (2016)

Mathematica Bohemica

Similarity:

The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and...

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

Similarity:

For a real number q > 1 and a positive integer m , let Y m ( q ) : = i = 0 n ϵ i q i : ϵ i 0 , ± 1 , ... , ± m , n = 0 , 1 , ... . In this paper, we show that Y m ( q ) is dense in if and only if q < m + 1 and q is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

A note on a property of the Gini coefficient

Marian Genčev (2019)

Communications in Mathematics

Similarity:

The scope of this note is a self-contained presentation of a mathematical method that enables us to give an absolute upper bound for the difference of the Gini coefficients G ( σ 1 , , σ n ) - G ( γ 1 , , γ n ) , where ( γ 1 , , γ n ) represents the vector of the gross wages and ( σ 1 , , σ n ) represents the vector of the corresponding super-gross wages that is used in the Czech Republic for calculating the net wage. Since (as of June 2019) σ i = 100 · 1 . 34 γ i / 100 , the study of the above difference seems to be somewhat inaccessible for many economists. However, our estimate...

An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

Marcin Dudziński (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let: 𝐘 = 𝐘 i , where 𝐘 i = Y i , 1 , . . . , Y i , d , i = 1 , 2 , , be a d -dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf F , and F n 𝐱 : = 1 n i = 1 n 𝕀 Y i , 1 x 1 , , Y i , d x d denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process B n = n F n - F under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.

Hilbert series of the Grassmannian and k -Narayana numbers

Lukas Braun (2019)

Communications in Mathematics

Similarity:

We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the q -Hilbert series is a Vandermonde-like determinant. We show that the h -polynomial of the Grassmannian coincides with the k -Narayana polynomial. A simplified formula for the h -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the k -Narayana numbers,...