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Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the Ramanujan 6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

A rule for polynomial computation which both reduces the number of necessary multiplications and results in less numerical instability due to potential subtraction of one ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

Let Q(x)=Q(x_1,x_2,...,x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be ...

A polynomial of the form f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 having coefficients a_i that are all integers. An integer polynomial gives integer values for all integer ...