Higher Residue Symbol

2011/05/04 by R. Balasubramanian, Balasubramanian, R., Prem Prakash Pandey +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1105.0912

arxiv created 2012/01/10 · arxiv updated 2012/01/11

Abstract

Given a prime number l and a finite set of integers S=\a₁,...,a_m\ we find out the exact degree of the extension ℚ(a₁^(1)/(l),...,a_m^(1)/(l))/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=\a₁,...,a_m\. This latter arguement enable one to describe the degree ℚ(a₁^(1)/(l),...,a_m^(1)/(l))/ℚ in much simpler terms.

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