Higher residue symbols

2011/03/01 by R. Balasubramanian, Balasubramanian, R., Prem Prakash Pandey +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1103.0110

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openalex publication_date 2011/03/01 · arxiv created 2011/05/04 · arxiv updated 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 two different ways to compute this degree. The first method is using ramifiaction theory. The second proof follwos from our study of the distribution of primes p for which all of a_i are l^th power residue simultaneously.

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