Quadratic reciprocity and Riemann’s non-differentiable function
نویسندگان
چکیده
منابع مشابه
Quadratic 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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We now come to the most important result in our course: the law of quadratic reciprocity, or, as Gauss called it, the aureum theorema (“golden theorem”). Many beginning students of number theory have a hard time appreciating this golden theorem. I find this quite understandable, as many first courses do not properly prepare for the result by discussing enough of the earlier work which makes qua...
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The character associated to a quadratic extension field K of Q, χ : Z −→ C, χ(n) = (disc(K)/n) (Jacobi symbol), is in fact a Dirichlet character; specifically its conductor is |disc(K)|. This fact encodes basic quadratic reciprocity from elementary number theory, phrasing it in terms that presage class field theory. This writeup discusses Hilbert quadratic reciprocity in the same spirit. Let k ...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2015
ISSN: 2363-9555
DOI: 10.1007/s40993-015-0015-5