Search Bounds for Zeros of Polynomials over the Algebraic Closure of Q

Height Bounds on Zeros of Quadratic Forms Over Q-bar

In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For a single quadratic form in N ≥ 2 variables on a subspace of Q , we prove an upper bound on the height of a smallest nontrivial zero outside of an algebraic set under the assumption that such a zero exists. For a system of k quadratic forms on an L-dimensional subspace of Q , N ≥ L ≥ k(k+1) 2 + 1,...

Domain of attraction of normal law and zeros of random polynomials

Let$ P_{n}(x)= sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraicpolynomial, where $A_{0},A_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus $A_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}H_{j}(t)}$, where $H_j(t)$'s are complex slowlyvarying functions.Under the assumption that there exist ...

On the average number of sharp crossings of certain Gaussian random polynomials

On the Real Zeros of Weighted q-Euler Polynomials

Using computer, a realistic study for new analogs of weighted q-Euler numbers and polynomials is very interesting. It is the aim of this paper to observe an interesting phenomenon of ‘scattering’ of the zeros of the weighted q-Euler polynomials E (α) n,q (x). The outline of this paper is as follows. In Section 2, we study weighted q-Euler polynomials E (α) n,q (x). In Section 3, we describe the...

An Approximation Algorithm for the Number of Zeros of Arbitrary Polynomials over GF[q]

We design the rst polynomial time (for an arbitrary and xed eld GFq]) (;)-approximation algorithm for the number of zeros of arbitrary polynomial f(x 1 ; : : :; x n) over GFq]. It gives the rst eecient method for estimating the number of zeros and nonzeros of multivariate polynomials over small nite elds other than GF2] (like GF3]), the case important for various circuit approximation technique...