ON THE dTH POWER RESIDUE SYMBOL OF FUNCTION FIELDS

Calculating the Power Residue Symbol and Ibeta

In the recent PhD thesis of Bouw, an algorithm is examined that computes the group structure of the principal units of a p-adic number €eld completion. In the same thesis, this algorithm is used to compute Hilbert norm residue symbols. In the present paper, we will demonstrate two other applications. Œe €rst application is the computation of an important invariant of number €eld completions, ca...

An Efficient Seventh Power Residue Symbol Algorithm

Power residue symbols and their reciprocity laws have applications not only in number theory, but also in other fields like cryptography. A crucial ingredient in certain public key cryptosystems is a fast algorithm for computing power residue symbols. Such algorithms have only been devised for the Jacobi symbol as well as for cubic and quintic power residue symbols, but for no higher powers. In...

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...

kTH POWER RESIDUE CHAINS OF GLOBAL FIELDS

In 1974, Vegh proved that if k is a prime and m a positive integer, there is an m term permutation chain of kth power residue for infinitely many primes [E.Vegh, kth power residue chains, J.Number Theory, 9(1977), 179-181]. In fact, his proof showed that 1, 2, 22, ..., 2m−1 is an m term permutation chain of kth power residue for infinitely many primes. In this paper, we prove that for k being a...

A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field