Let Q(ζ) be the cyclotomic field obtained from Q by adjoining a primitive seventh root of unity ζ. Normalized primary elements of this field are characterized and related to Jacobi sums and to solutions of a system of quadratic Diophantine equations of Dickson type involving a rational prime p ≡ 1 (mod 7). These objects and their connection are then used to give another formulation of the compl...

Let p ≡ 1 (mod 4) be a prime number and let ζ = e be a primitive root of unity. Then there exists a unique biquadratic extension eld Q(y)/Q that is a sub eld of Q(ζ). The aim of this work is to construct an algorithm for nding such y explicitly. Finally we state a general conjecture about the y we found.

In this paper, we show that the problem of computing the complex roots of unity is not as simple as it seems at rst. In particular, the formulas given in a standard programmer's reference book Knuth, Seminumerical Algorithms, 1981] are shown to be numerically unstable , giving unacceptably large error for moderate sized sequences. We give alternative formulas, which we show to be superior both ...

Let L/K be an abelian extension of number fields. We prove an uniform lower bound for the height in L∗ outside roots of unity. This lower bound depends only on the degree [L : K].

Medical imaging has a remarkable role in the practice of clinical medicine. This study intends to evaluate the knowledge of indications of five common medical imaging modalities and estimation of the imposed cost of their non-indicated requests among medical students who attend Shiraz University of Medical Sciences, Shiraz, Iran. We conducted across-sectional survey using a self-administered qu...

While the COVID-19 pandemic was initially rooted in social unity and acceptance of lockdown procedures, long-standing distancing measures have kept students out physical classroom on off for nearly two years. The instability transitions outcomes remote learning has gained attention, mainly as frustrations over increased transmission rates subsequent quarantines occur. Evidence shown that had ne...

meaning of islamic unity in two internal & external levels of diplomatic idea of islam has superior place. present situation of world of islam and various devilish plots for provoking disputes and enmity among the muslims shows well the necessity of this issue. undoubtedly, the survey of valuable experience of leaders of islamic world unity at present age, especially survey of seyed jamal al-di...