Description

• Title:
  An elementary proof of the d-th power reciprocity law over function fields
• Creator:
  Blaszczok, Anna
• Description:
  This paper generalises the proof of quadratic reciprocity law in 𝔽q[T] presented by Chun-Gang Ji and Yan Xue [2] to the case of d-th power residues, where d divides the order of 𝔽*q. Using only elementary properties of finite fields and basic number-theoretic tools we show that if P,Q∈𝔽q[T] are distinct irreducible polynomials then(P/Q)d = (-1)q-1/ddeg(P)deg(Q)(Q/P)d,where (P/Q)d is the d-th power residue symbol.
• Object availability:
  free access
• Date:
  2011.09.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 25 (2011); 49-57;
  Annales Mathematicae Silesianae; Tom 25 (2011); 49-57;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/14021/10728
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/14021
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other