On quadratic reciprocity over function fields
نویسندگان
چکیده
منابع مشابه
An Elementary Proof of the Law of Quadratic Reciprocity over Function Fields
Let P and Q be relatively prime monic irreducible polynomials in Fq [T ] (2 q). In this paper, we give an elementary proof for the following law of quadratic reciprocity in Fq [T ]: ( Q P )( P Q ) = (−1) |P |−1 2 |Q|−1 2 , where ( Q P ) is the Legendre symbol.
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متن کاملQuadratic Reciprocity
Quadratic Reciprocity is arguably the most important theorem taught in an elementary number theory course. Since Gauss’ original 1796 proof (by induction!) appeared, more than 100 different proofs have been discovered. Here I present one proof which is not particularly well-known, due to George Rousseau [2]. (The proof was rediscovered more recently by (then) high-schooler Tim Kunisky [1].) Alt...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1996
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1996.173.147