An example of a computable absolutely normal number
... Moreover, every rational r is not normal to any base q ≥ 2 [4]: the fractional expansion of r in base q will eventually repeat, say with a period of k, in which case the number r is about as far as being normal to the base q k as it can be. The first example of an absolutely normal number was given ...
... Moreover, every rational r is not normal to any base q ≥ 2 [4]: the fractional expansion of r in base q will eventually repeat, say with a period of k, in which case the number r is about as far as being normal to the base q k as it can be. The first example of an absolutely normal number was given ...
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4.1 Reduction theory
... Lagrange introduced the notion of reduced forms, and the point is the following. Theorem 4.1.6. Any (positive definite) form Q is properly equivalent to a unique reduced form. Proof. First we will show Q is properly equivalent to a reduced form ax2 + bxy + cy 2 . Suppose |b| is minimal such that the ...
... Lagrange introduced the notion of reduced forms, and the point is the following. Theorem 4.1.6. Any (positive definite) form Q is properly equivalent to a unique reduced form. Proof. First we will show Q is properly equivalent to a reduced form ax2 + bxy + cy 2 . Suppose |b| is minimal such that the ...
