Power Residue Character of Rational Primes

Charles Helou; Ron Roll; Lawrence C. Washington

Vol 16, No 1 (2001)
Pages: 19-37
Published: 2001-03-01

Power Residue Character of Rational Primes

Charles Helou ¹, Ron Roll ², Lawrence C. Washington ³

Affiliations
1 Penn State Univ., 25 Yearsley Mill Rd, Media, PA 19063, United States
2 3804 Kelsey St., Silver Spring, MD 20906, United States
3 Univ. of Maryland, College Park, MD 20742, United States

Let p and q be two odd prime numbers such that q ≡ 1 (mod p) and q is the norm in ℚ(ℂ_p)/ℚ of some element α in ℤ[ℂp], where ζp is a primitive p-th ischolar_main of unity. Many authors have given criteria for a rational prime r ≠ p, q to be a p -th power residue modulo q. We give a unified approach to such results and obtain criteria in terms of α. These are applied to some simple cases.