Higher Residue Symbol

Details Higher Residue Symbol Higher Residue Symbol

2011-05-04

arxiv.org/abs/1105.0912v3

Mathematics

Number Theory

Scientific paper

Given a prime number $l$ and a finite set of integers $S=\{a_1,...,a_m\}$ we find out the exact degree of the extension $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$. We give an algorithm to compute this degree and then further relate it to the study of the distribution of primes $p$ for which all of $a_i$ assume a preassigned $l^{th}$ power residue simultaneously. Also we relate this degree to rank of a matrix obtained from $S=\{a_1,...,a_m\}$. This latter arguement enable one to describe the degree $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$ in much simpler terms.

Affiliated with

Also associated with

No associations

Rating

Higher Residue Symbol does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Higher Residue Symbol, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher Residue Symbol will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-689955