The Conway–Sloane calculus for 2-adic lattices
نویسندگان
چکیده
منابع مشابه
The Conway-sloane Calculus for 2-adic Lattices
We develop the notational system developed by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used for many years, but it seems that no proof has been published before now. Throughout, an integer means an element of the ring Z2 of 2-adic integers, and we wri...
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The p-adic integrals evaluated here were explicitly introduced only in the later 20th century, starting with Tate and Iwasawa in 1950, by MacDonald in the 1950s, in the 1960’s by Gelfand and Piatetski-Shapiro, Jacquet, Shalika, and then by Jacquet-Langlands in 1970, although shadows of them appeared long ago in the work of Lagrange, Legendre, Gauss, Galois, and Dirichlet. From our vantage, they...
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A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for algebraic independence by the well-known Jacobian criterion. For fields of other characteristic p > 0, no analogous characterization is known. In this paper we give the first such criterion. Essentially, it boils down to a non-degeneracy condition on a lift of the Jacobian polynomial over (an unra...
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ژورنال
عنوان ژورنال: L’Enseignement Mathématique
سال: 2020
ISSN: 0013-8584
DOI: 10.4171/lem/66-1/2-2