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The deepest input will be Lemma 2.1 be- low which only requires pre-Prime Number Theorem elementary methods for its proof (in Tenenbaum’s [11] introductory book on analytic
This deformation ring ought to be isomorphic to a certain ring generated by Hecke operators, whose tangent space can be related to the modular degree, at least if we assume that it is
Ces conjectures semblent pour l’ins- tant hors de port´ee dans toute leur g´en´eralit´e, mais on sait en d´emontrer certains cas particuliers ; ce sera l’objet du paragraphe 2..
Given a solubility certificate, one can quickly find such ( X, Y, Z ) with the LLL lattice reduction algorithm (see [LLL82]) and Lemma 2.7 in [CR03] (where an even faster algorithm
The converse of Proposition 3.3 is false; i.e., continuous spectrally dominant sub- norms on subsets of F n × n which are closed under scalar multiplication and under.. raising
Our second con- struction produces a ( −J )-type tournament matrix from two minimum rank tourna- ment matrices of even orders..
Note that also in the time inhomogeneous case the time dependent Dirichlet form is controlled, uniformly in time, by the Dirichlet form of the simple random walk, and therefore
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribu- tion and two-parameter Dirichlet process when parameter θ approaches infinity. The