Journal of the Ramanujan Mathematical Society

Abstract

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.

AMS (2000) Subject Classification. 11A15, 11R18.

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