Simple zeros of degree 2 $L$-functions

Andrew R. Booker

Displaying similar documents to “Simple zeros of degree 2 $L$ -functions”

A note on the number of zeros of polynomials in an annulus

Xiangdong Yang, Caifeng Yi, Jin Tu (2011)

Annales Polonici Mathematici

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Let p(z) be a polynomial of the form $p (z) = \sum_{j = 0}^{n} a_{j} z^{j}$ , $a_{j} \in - 1, 1$ . We discuss a sufficient condition for the existence of zeros of p(z) in an annulus z ∈ ℂ: 1 - c < |z| < 1 + c, where c > 0 is an absolute constant. This condition is a combination of Carleman’s formula and Jensen’s formula, which is a new approach in the study of zeros of polynomials.

Zeros of functions in $D^{p, α}$ spaces

M. Jevtić (1981)

Matematički Vesnik

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Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation

Innocent Ndikubwayo (2020)

Czechoslovak Mathematical Journal

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This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence ${P_{i}}_{i = 1}^{\infty}$ generated by a three-term recurrence relation $P_{i} (x) + Q_{1} (x) P_{i - 1} (x) + Q_{2} (x) P_{i - 2} (x) = 0$ with the standard initial conditions $P_{0} (x) = 1, P_{- 1} (x) = 0,$ where $Q_{1} (x)$ and $Q_{2} (x)$ are arbitrary real polynomials.

Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu, Cai-Feng Yi (2010)

Annales Polonici Mathematici

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We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $f^{(k)} + a_{k - 1} (z) f^{(k - 1)} + \dots + a ₁ (z) f^{'} + D (z) f = 0$ , (1) where $D (z) = Q ₁ (z) e^{P ₁ (z)} + Q ₂ (z) e^{P ₂ (z)} + Q ₃ (z) e^{P ₃ (z)}$ , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), $a_{j} (z)$ (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

Real zeros of general $L$ -functions

Alberto Perelli, Giuseppe Puglisi (1981)

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

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In questo lavoro vengono studiati gli zeri reali di una classe di serie di Dirichlet, che generalizzano le funzioni $L(s,\chi)$ , definite in [8], Combinando le tecniche elementari di Pintz [9] con alcuni metodi analitici si ottiene l’estensione dei classici teoremi di Hecke e Siegel.

Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. K. Dewan, Sunil Hans (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we obtain certain results for the polar derivative of a polynomial $p (z) = c_{n} z^{n} + \sum_{j = μ}^{n} c_{n - j} z^{n - j}$ , $1 \leq μ \leq n$ , having all its zeros on $| z | = k$ , $k \leq 1$ , which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros. [Editor’s note: There are flaws in the paper, see M. A. Qazi, Remarks on some recent results about polynomials with restricted zeros, Ann. Univ. Mariae Curie-Skłodowska Sect. A 67 (2), (2013),...

On distance between zeros of solutions of third order differential equations

N. Parhi, S. Panigrahi (2001)

Annales Polonici Mathematici

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The lower bounds of the spacings b-a or a’-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form y”’ + q(t)y’ + p(t)y = 0 (*) are derived under very general assumptions on p and q. These results are then used to show that $t_{n + 1} - t ₙ \to \infty$ or $t_{n + 2} - t ₙ \to \infty$ as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a...

The Lehmer constants of an annulus

Artūras Dubickas, Chris J. Smyth (2001)

Journal de théorie des nombres de Bordeaux

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Let $M (α)$ be the Mahler measure of an algebraic number $α$ , and $V$ be an open subset of $ℂ$ . Then its $L (V)$ is inf $M {(α)}^{1 / deg (α)}$ , the infimum being over all non-zero non-cyclotomic $α$ lying with its conjugates outside $V$ . We evaluate $L (V)$ when $V$ is any annulus centered at $0$ . We do the same for a variant of $L (V)$ , which we call the transfinite Lehmer constant $L_{\infty} (V)$ .Also, we prove the converse to Langevin’s Theorem, which states that $L (V) > 1$ if $V$ contains a point of modulus $1$ . We prove the corresponding result for...

Uniqueness results for differential polynomials sharing a set

Soniya Sultana, Pulak Sahoo (2025)

Mathematica Bohemica

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We investigate the uniqueness results of meromorphic functions if differential polynomials of the form ${(Q (f))}^{(k)}$ and ${(Q (g))}^{(k)}$ share a set counting multiplicities or ignoring multiplicities, where $Q$ is a polynomial of one variable. We give suitable conditions on the degree of $Q$ and on the number of zeros and the multiplicities of the zeros of $Q^{'}$ . The results of the paper generalize some results due to T. T. H. An and N. V. Phuong (2017) and that of N. V. Phuong (2021).

On zeros of differences of meromorphic functions

Yong Liu, HongXun Yi (2011)

Annales Polonici Mathematici

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Let f be a transcendental meromorphic function and $g (z) = f (z + c ₁) + \dots + f (z + c_{k}) - k f (z)$ and $g_{k} (z) = f (z + c ₁) \dots f (z + c_{k}) - f^{k} (z)$ . A number of results are obtained concerning the exponents of convergence of the zeros of g(z), $g_{k} (z)$ , g(z)/f(z), and $g_{k} (z) / f^{k} (z)$ .

On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas

Igor E. Shparlinski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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For a prime p > 2, an integer a with gcd(a,p) = 1 and real 1 ≤ X,Y < p, we consider the set of points on the modular hyperbola $_{a, p} (X, Y) = (x, y) : x y \equiv a (m o d p), 1 \leq x \leq X, 1 \leq y \leq Y$ . We give asymptotic formulas for the average values $\sum_{\begin{matrix} ( \end{matrix} x, y) \in_{a, p} (X, Y) x \neq y *} φ (| x - y |) / | x - y |$ and $\sum_{\begin{matrix} ( \end{matrix} x, y) \in_{a, p} (X, X) x \neq y *} φ (| x - y |)$ with the Euler function φ(k) on the differences between the components of points of $_{a, p} (X, Y)$ .

Sharp estimation of the coefficients of bounded univalent functions close to identity

Lucjan Siewierski

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CONTENTSIntroduction...............................................................................................................................................................................5Definitions and notation.........................................................................................................................................................7The main result........................................................................................................................................................................91....

The zeros of functions of finite order in $C^{n}$

Lawrence Gruman (1983)

Annales Polonici Mathematici

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Real zeros of general $L$ -functions

Alberto Perelli, Giuseppe Puglisi (1981)

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

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Zeros of a certain class of Gauss hypergeometric polynomials

Addisalem Abathun, Rikard Bøgvad (2018)

Czechoslovak Mathematical Journal

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We prove that as $n \to \infty$ , the zeros of the polynomial $_{2} F_{1} [\begin{matrix} - n, α n + 1 \\ α n + 2 \end{matrix}; z]$ cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter $α$ and partially proves a conjecture made by the authors in an earlier work.

On automatic boundedness of Nemytskiĭ set-valued operators

S. Rolewicz, Wen Song (1995)

Studia Mathematica

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Let X, Y be two separable F-spaces. Let (Ω,Σ,μ) be a measure space with μ complete, non-atomic and σ-finite. Let $N_{F}$ be the Nemytskiĭ set-valued operator induced by a sup-measurable set-valued function $F : Ω \times X \to 2^{Y}$ . It is shown that if $N_{F}$ maps a modular space $(N (L (Ω, Σ, μ; X)), ϱ_{N, μ})$ into subsets of a modular space $(M (L (Ω, Σ, μ; Y)), ϱ_{M, μ})$ , then $N_{F}$ is automatically modular bounded, i.e. for each set K ⊂ N(L(Ω,Σ,μ;X)) such that $r_{K} = s u p ϱ_{N, μ} (x) : x \in K < \infty$ we have $s u p ϱ_{M, μ} (y) : y \in N_{F} (K) < \infty$ .

Some Results on the Properties of Differential Polynomials Generated by Solutionsof Complex Differential Equations

Zinelâabidine LATREUCH, Benharrat BELAÏDI (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper is devoted to considering the complex oscillation of differential polynomials generated by meromorphic solutions of the differential equation $f^{(k)} + A_{k - 1} (z) f^{(k - 1)} + \dots + A_{1} (z) f^{'} + A_{0} (z) f = 0,$ where $A_{i} (z)$ $(i = 0, 1, \dots, k - 1)$ are meromorphic functions of finite order in the complex plane.

Displaying similar documents to “Simple zeros of degree 2 L -functions”

Displaying similar documents to “Simple zeros of degree 2 $L$ -functions”