Power Reciprocity for Binomial Cyclotomic Integers

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We give an explicit expression for the inversion factor (α/β)l(β/α)-1lof thelth power residue symbol over the cyclotomic field of l th roots of unity, whenαandβare binomial cyclotomic integersx+yζnrelatively prime to each other and tol. Herelis an odd prime number,ζa primitivelth root of unity andx, y∈Z We note that Eisenstein's reciprocity law extends to the case where primary binomial integers replace rational integers. As an application, we obtain necessary and sufficient congruence conditions for a rational integer to be anlth power residue modulo some prime numbers of the form (xl+1)/(x+1).

Original languageEnglish (US)
Pages (from-to)245-256
Number of pages12
JournalJournal of Number Theory
Volume71
Issue number2
DOIs
StatePublished - Aug 1998

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Power Reciprocity for Binomial Cyclotomic Integers'. Together they form a unique fingerprint.

Cite this