Related papers: Zeros of Fekete polynomials

Let $f_1,\dots,f_k\in\mathbb{R}[X]$ be polynomials of degree at most $d$ with $f_1(0)=\dots=f_k(0)=0$. We show that there is an integer $n<x$ such that the fractional parts $\|f_i(n)\|\ll x^{c/k}$ for all $1\le i\le k$ and for some constant…

We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure $z^{\omega-1}\mathrm{d} z$, where $\omega\in\mathbb{R}\setminus\{0\}$. We derive their explicit form, a generating function and several…

In this paper we investigate distribution of zeros for only quasipolynom and obtain exactly lower-bound for their modulus.

We study equidistribution problem of zeros in relation to a sequence of $Z$-asymptotically Chebyshev polynomials on $\mathbb{C}^{m}$. We use certain results obtained in a very recent work of Bayraktar, Bloom and Levenberg and have an…

We study the zeros of cusp forms of large weight for the modular group, which have a very large order of vanishing at infinity, so that they have a fixed number D of finite zeros in the fundamental domain. We show that for large weight the…

We study the simultaneous zeros of a random family of $d$ polynomials in $d$ variables over the $p$-adic numbers. For a family of natural models, we obtain an explicit constant for the expected number of zeros that lie in the $d$-fold…

A classical result of Erdos and Turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using…

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent…

It is well known that for every $f\in C^m$ there exists a polynomial $p_n$ such that $p^{(k)}_n\rightarrow f^{(k)}$, $k=0,\ldots,m$. Here we prove such a result for fractional (non-integer) derivatives. Moreover, a numerical method is…

We study the asymptotic distribution of the number $Z_{N}$ of zeros of random trigonometric polynomials of degree $N$ as $N\to\infty$. It is known that as $N$ grows to infinity, the expected number of the zeros is asymptotic to…

The current research regarding the Riemann zeros suggests the existence of a non-trivial algebraic/analytic structure on the set of Riemann zeros. The duality between primes and Riemann zeta function zeros suggests some new goals and…

Addressing a problem posed by W. Li and A. Wei (2009), we investigate the average number of (complex) zeros of a random harmonic polynomial $p(z) + \overline{q(z)}$ sampled from the Kac ensemble, i.e., where the coefficients are independent…

We study asymptotic distribution of zeros of random holomorphic sections of high powers of positive line bundles defined over projective homogenous manifolds. We work with a wide class of distributions that includes real and complex…

The purpose of this note is to revive in $L^p$ spaces the original A. Markov ideas to study monotonicity of zeros of orthogonal polynomials. This allows us to prove and improve in a simple and unified way our previous result [Electron.…

We consider integer recurrences of the form a_n = f(a_{n-1}), where f is a quadratic polynomial with integer coefficients. We show, for four infinite families of f, that the set of primes dividing at least one term of such a sequence must…

In this work, we are dealing with some properties relating the zeros of a polynomial and its Mahler measure. We provide estimates on the number of real zeros of a polynomial, lower bounds on the distance between the zeros of a polynomial…

We consider almost-primes of the form $f(p)$ where $f$ is an irreducible polynomial over $\mathbb Z$ and $p$ runs over primes. We improve a result of Richert for polynomials of degree at least $3$. In particular we show that, when the…

Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…

The relationship between a polynomial's zeros and factors is well known. If a is a zero of f(x) then (x-a) is a factor of f(x). In this paper, we generalize this idea to polynomials of two variables and with real coefficients. We consider…

We consider the problem whether the ordinates of the non-trivial zeros of $\zeta(s)$ are uniformly distributed modulo the Gram points, or equivalently, if the normalized zeros $(x_n)$ are uniformly distributed modulo 1. Odlyzko conjectured…