A NON CONCENTRATION ESTIMATE FOR RANDOM MATRIX
... trivially. This ends the proof. The case of the hyperplane is analogous. Proof of Theorem 3.1. As already mentioned, in the case when the proximal dimension of Gµ is one, then the theorem is well-known. See for example [5, Theorem 8.1(iii)] for a proof. It is also well-known if the proximal dimens ...
... trivially. This ends the proof. The case of the hyperplane is analogous. Proof of Theorem 3.1. As already mentioned, in the case when the proximal dimension of Gµ is one, then the theorem is well-known. See for example [5, Theorem 8.1(iii)] for a proof. It is also well-known if the proximal dimens ...
SOME PARI COMMANDS IN ALGEBRAIC NUMBER
... bnfinit(f(x)).fu gives the fundamental units of Kf , expressed as polynomials in x mod f (x). bnfreg(f(x)) gives the regulator of Kf . dirzetak(nfinit(f(x)),N) gives the coefficients of the first N terms in the Dirichlet series for Kf when it is written as a sum over positive integers. That is, if ζ ...
... bnfinit(f(x)).fu gives the fundamental units of Kf , expressed as polynomials in x mod f (x). bnfreg(f(x)) gives the regulator of Kf . dirzetak(nfinit(f(x)),N) gives the coefficients of the first N terms in the Dirichlet series for Kf when it is written as a sum over positive integers. That is, if ζ ...