270 research outputs found

    Modular forms and elliptic curves over the cubic field of discriminant -23

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    Let F be the cubic field of discriminant -23 and let O be its ring of integers. By explicitly computing cohomology of congruence subgroups of GL(2,O), we computationally investigate modularity of elliptic curves over F.Comment: Incorporated referee's comment

    Perfect forms over totally real number fields

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    A rational positive-definite quadratic form is perfect if it can be reconstructed from the knowledge of its minimal nonzero value m and the finite set of integral vectors v such that f(v) = m. This concept was introduced by Voronoi and later generalized by Koecher to arbitrary number fields. One knows that up to a natural "change of variables'' equivalence, there are only finitely many perfect forms, and given an initial perfect form one knows how to explicitly compute all perfect forms up to equivalence. In this paper we investigate perfect forms over totally real number fields. Our main result explains how to find an initial perfect form for any such field. We also compute the inequivalent binary perfect forms over real quadratic fields Q(\sqrt{d}) with d \leq 66.Comment: 11 pages, 2 figures, 1 tabl

    On the discussion of fidelity to and validity of Nazi Laws

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    AN INTERPRETATION OF “NATURE" UNDERLYING THE LAW

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    LEGAL FORMALISM RECONSIDERED

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