Decomposition of primes in number fields defined by trinomials

Decomposition of primes in number fields defined by trinomials

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

Bounded Gaps between Primes in Number Fields and Function Fields

The Hardy–Littlewood prime k-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress toward this problem. In this work, we extend the Maynard-Tao method to both number fields and the function field Fq(t).

Circular sets of primes of imaginary quadratic number fields

Let p be an odd prime number and let K be an imaginary quadratic number field whose class number is not divisible by p. For a set S of primes of K whose norm is congruent to 1 modulo p, we introduce the notion of strict circularity. We show that if S is strictly circular, then the group G(KS(p)/K) is of cohomological dimension 2 and give some explicit examples.

The Number of Ramified Primes in Number Fields of Small Degree

In this paper we investigate the distribution of the number of primes which ramify in number fields of degree d ≤ 5. In analogy with the classical Erdős-Kac theorem, we prove for Sd-extensions that the number of such primes is normally distributed with mean and variance log log X.