منابع مشابه
Reciprocity Laws
Informal notes for a talk at UNCG on reciprocity laws (such as quadratic reciprocity and Shimura-Taniyama). This material is from Fearless Symmetry by Ash and Gross [1] and Galois Representations and Modular Forms by Ribet [2].
متن کاملGeneralized Non-abelian Reciprocity Laws: a Context for Wiles’s Proof
In as elementary a way as possible, we place Wiles’s proof of Fermat’s Last Theorem into the context of a general description of reciprocity conjectured to obtain between algebraic varieties defined over Q and Hecke eigenvectors in the homology of the spaces of lattices in R. We shall find the Cube of the Rainbow, Of that, there is no doubt. But the Arc of a Lover’s conjecture Eludes the findin...
متن کاملGeneralized Reciprocity Laws for Sums of Harmonic Numbers
We present summation identities for generalized harmonic numbers, which generalize reciprocity laws discovered when studying the algorithm quickselect. Furthermore, we demonstrate how the computer algebra system Sigma can be used in order to find/prove such identities. We also discuss alternating harmonic sums, as well as limiting relations.
متن کاملRational Reciprocity Laws
The purpose of this note is to provide an overview of Rational Reciprocity (and in particular, of Scholz’s reciprocity law) for the non-number theorist. In the first part, we will describe the background in number theory that will be necessary for a complete understanding of the material to be discussed in the second part. The second part focuses on a proof of Scholz’s reciprocity law using the...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04554-6