An elementary proof of the d-th power reciprocity law over function fields

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DC pole	Wartość	Język
dc.contributor.author	Blaszczok, Anna	-
dc.date.accessioned	2018-06-25T19:42:30Z	-
dc.date.available	2018-06-25T19:42:30Z	-
dc.date.issued	2011	-
dc.identifier.citation	Annales Mathematicae Silesianae, [Nr] 25 (2011), s. 49-57	pl_PL
dc.identifier.issn	0860-2107	-
dc.identifier.issn	2391-4238	-
dc.identifier.uri	http://hdl.handle.net/20.500.12128/4920	-
dc.description.abstract	This paper generalises the proof of quadratic reciprocity law in Fq[T] presented by C. G. Ji and Y. Xue [Proc. Amer. Math. Soc. 136 (2008), no. 9, 3035–3039; MR2407064] 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 (PQ)d=(−1)q−1ddeg(P)deg(Q)(QP)d, where (PQ)d is the d-th power residue symbol	pl_PL
dc.language.iso	en	pl_PL
dc.rights	Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/pl/	*
dc.subject	Polynomial ring	pl_PL
dc.subject	d-th power residue	pl_PL
dc.subject	Reciprocity law	pl_PL
dc.title	An elementary proof of the d-th power reciprocity law over function fields	pl_PL
dc.type	info:eu-repo/semantics/article	pl_PL
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