As automorphic L-functions or Artin L-functions, several classes of Lfunctions have Euler products and functional equations. In this paper we study the zeros of L-functions which have the Euler products and functional equations. We show that there exists some relation between the zeros of the Riemann zetafunction and the zeros of such L-functions. As a special case of our results, we find the r...

This paper studies zeros of networked linear systems with time-invariant interconnection topology. While the characterization of zeros is given for both heterogeneous and homogeneous networks, homogeneous networks are explored in greater detail. In the current paper, for homogeneous networks with time-invariant interconnection dynamics, it is illustrated how the zeros of each individual agent’s...

Al~lract--Motivated by a crucial role blocking zeros play in deciphering the strong stabilizability of a given system, a careful study of blocking zeros is undertaken here. After developing certain properties of blocking zeros and based on the multiplicity structure of invariant zeros, we identify what kind of invariant zeros are blocking zeros. For controllable and observable systems, an invar...

which is valid for any complex s, it follows that ζ(s) has zeros at s = −2,−4, . . . . These zeros are called the “trivial” zeros of ζ(s), to distinguish them from the complex zeros of ζ(s). The zeta-function has also an infinity of complex zeros. It is well-known that all complex zeros of ζ(s) lie in the so-called “critical strip” 0 < σ = R s < 1, and if N(T ) denotes the number of zeros ρ = β...

One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...

This survey paper is devoted to inequalities for zeros of algebraic polynomials. We consider the various bounds for the moduli of the zeros, some related inequalities, as well as the location of the zeros of a polynomial, with a special emphasis on the zeros in a strip in the complex plane.

We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them.

For a given real entire function φ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions Q = (φ/φ) and Q1 = (φ /φ). This connection leads to a proof of the Hawaii conjecture [T.Craven, G.Csordas, and W. Smith, The zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math. (2) 125 (1987), 405–431] stating that th...

We study the Yang-Lee zeros of a random matrix partition function with the global symmetries of the QCD partition function. We consider both zeros in the complex chemical potential plane and in the complex mass plane. In both cases we find that the zeros are located on a curve. In the thermodynamic limit, the zeros appear to merge to form a cut. The shape of this limiting curve can be obtained ...

We examine the electrostatic properties of exceptional and regular zeros of Xm-Laguerre and Xm-Jacobi polynomials. Since there is a close connection between the electrostatic properties of the zeros and the stability of interpolation on the system of zeros, we can deduce an Egerváry-Turán type result as well. The limit of the energy on the regular zeros is also investigated.