We describe the classical Hasse principle for the existence of nontrivial zeros for quadratic forms over number fields, namely, local zeros over all completions at places of the number field imply nontrivial zeros over the number field itself. We then go on to explain more general questions related to the Hasse principle for nontrivial zeros of quadratic forms over function fields, with referen...

We describe computations which show that each of the first 12069 zeros of the Ramanujan τ -Dirichlet series of the form σ + it in the region 0 < t < 6397 is simple and lies on the line σ = 6. The failures of Gram’s law in this region are also noted. The first 5018 zeros and 2228 successive zeros beginning with the 20001st zero are also calculated. The distribution of the normalized spacing of t...

Dynamical quantum phase transitions are at the forefront of current efforts to understand matter out equilibrium. Except for a few exactly solvable models, predictions these critical phenomena typically rely on advanced numerical methods. However, those approaches mostly restricted one dimension, making investigations two-dimensional systems highly challenging. Here, we present evidence dynamic...

Consider repeated measures data with many zeros. For the case with one grouping factor and one repeated measure, we examine several models, assuming that the nonzero data are roughly lognormal. One of the simplest approaches is to model the zeros as left-censored observations from the lognormal distribution. A random effect is assumed for subjects. The censored model makes a strong assumption a...

Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed....

We describe computations which show that each of the first 12069 zeros of the Ramanujan τ -Dirichlet series of the form σ + it in the region 0 < t < 6397 is simple and lies on the line σ = 6. The failures of Gram’s law in this region are also noted. The first 5018 zeros and 2228 successive zeros beginning with the 20001st zero are also calculated. The distribution of the normalized spacing of t...

This paper describes efficient algorithms for the computation of dominant zeros of large scale transfer functions. The transfer function zeros are demonstrated to be equal to the poles of a new inverse system, which is valid even for the strictly proper case. This is a new finding, which is important from practical as well as theoretical viewpoints. Hence, the dominant zeros can be computed as ...

The complex field zeros of the Random Energy Model are analytically determined. For T < Tc they are distributed in the whole complex plane with a density that decays very fast with the real component of H. For T > Tc a region is found which is free of zeros and is associated to the paramagnetic phase of the system. This region is separated from the former by a line of zeros. The real axis is fo...

Over the past ten years, many examples of natural polynomial families from combinatorics and number theory have emerged whose zeros for high degrees appear to converge to intriguing curves in the complex plane. One interesting collection of examples appears on the website [16] of Richard Stanley which includes chromatic polynomials of complete partite graphs, q-analogue of Catalan numbers, Bern...

Inequalities satisfied by the zeros of the solutions of second order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among o...