On polynomial reciprocity law

Chih Nung Hsu*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

The well-known law of quadratic reciprocity has over 150 proofs in print. We establish a relation between polynomial Jacobi symbols and resultants of polynomials over finite fields. Using this relation, we prove the polynomial reciprocity law and obtain a polynomial analogue of classical Burde's quartic reciprocity law. Under the use of our polynomial Poisson summation formula and the evaluation of polynomial exponential map, we get a reciprocity for the generalized polynomial quadratic Gauss sums.

原文英語
頁(從 - 到)13-31
頁數19
期刊Journal of Number Theory
101
發行號1
DOIs
出版狀態已發佈 - 2003 七月 1

ASJC Scopus subject areas

  • 代數與數理論

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