The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On L × L self-dual lattices studied (L ≤ 8), no Fisher zero lies on the unit circle p0 = e iθ in the complex p = (e − 1)/√Q plane for Q < 1, while some of the Fisher zeros lie on the unit circle for Q > 1 and the number ...

Recently the existence of certain SU(2) BPS monopoles with the symmetries of the Platonic solids has been proved. Numerical results in an earlier paper suggest that one of these new monopoles, the tetrahedral 3-monopole, has a remarkable new property, in that the number of zeros of the Higgs field is greater than the topological charge (number of monopoles). As a consequence, zeros of the Higgs...

Since B (s) and d(s) are coprime, the proof is complete. From the lemma, the blocking zeros are seen to coincide with the roots, counting multiplicities, of q(s) = 0. For the sake of comparison, we remark that Rosenbrock [3] defines the zeros of G(s) to be the roots of cl(s)cz(s). . c,(s)=O. Desoer and Schulman [ I ] and Wolovich [2], without specifying multiplicities, identify the roots of c,...

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...

In this paper we consider the numerical problems faced by a blind dereverberation algorithm based on a multi-channel linear prediction. One hypothesis frequently incorporated in multimicrophone dereverberation algorithms is that channels do not share common zeros. However, it is known that real room transfer functions have a large number of zeros close to the unit circle on the z-plane, and thu...

We study the variation of the zeros of the Hermite function Hλ(t) with respect to the positive real variable λ. We show that, for each nonnegative integer n, Hλ(t) has exactly n + 1 real zeros when n < λ ≤ n + 1 and that each zero increases from −∞ to ∞ as λ increases. We establish a formula for the derivative of a zero with respect to the parameter λ; this derivative is a completely monotonic ...

We explore the effect of zeros at the central point on nearby zeros of elliptic curve L-functions, especially for one-parameter families of rank r over Q. By the Birch and Swinnerton Dyer Conjecture and Silverman’s Specialization Theorem, for t sufficiently large the L-function of each curve Et in the family has r zeros (called the family zeros) at the central point. We observe experimentally a...

Stieltjes’ Theorem (cf. [11]) proves that if {pn}n=0 is an orthogonal sequence, then between any two consecutive zeros of pk there is at least one zero of pn for all positive integers k, k < n; a property called Stieltjes interlacing. We prove that Stieltjes interlacing extends across different sequences of Laguerre polynomials Ln, α > −1. In particular, we show that Stieltjes interlacing holds...

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2 + iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riem...

The distribution of partition function zeros of the two-dimensional Ising model in the complex temperature plane is studied within the context of triangular decorated lattices and their triangle-star transformations. Exact recursion relations for the zeros are deduced for the description of the evolution of the distribution of the zeros subject to the change of decoration level. In the limit of...