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Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...

On a Riemannian manifold M, there is a canonical connection called the Levi-Civita connection (pronounced lē-vē shi-vit-e), sometimes also known as the Riemannian connection ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

The number 163 is very important in number theory, since d=163 is the largest number such that the imaginary quadratic field Q(sqrt(-d)) has class number h(-d)=1. It also ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

Take K a number field and L an Abelian extension, then form a prime divisor m that is divided by all ramified primes of the extension L/K. Now define a map phi_(L/K) from the ...